Suppose we have an biased quarter that has a 0.3 probability of landing on heads. Suppose we flip the quarter independently 50 times and let A be the number of heads we observe. Apply Chebyshev's inequality to upper bound the probability P[A ≥30] and apply Markov's inequality to upper bound the probability P[A≥30]
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Applying Chebyshev's inequality, we find that P[A ≥ 30] is upper bounded by approximately 0.122, and applying Markov's inequality, we find that P[A ≥ 30] is upper bounded by 0.5.
To apply Chebyshev's inequality and Markov's inequality to upper bound the probability P[A ≥ 30], where A is the number of heads obtained when flipping a biased quarter 50 times, we need to know the mean and variance of A.
The mean (μ) of A can be calculated as the product of the number of trials (n) and the probability of success (p). In this case, n = 50 (number of flips) and p = 0.3 (probability of heads):
μ = np = 50 * 0.3 = 15
The variance (σ^2) of A can be calculated as the product of the number of trials (n), the probability of success (p), and the probability of failure (q = 1 - p):
σ^2 = npq = 50 * 0.3 * (1 - 0.3) = 10.5
Now we can apply Chebyshev's inequality and Markov's inequality to bound the probability P[A ≥ 30]:
Chebyshev's Inequality:
For any positive value k, the probability that a random variable X deviates from its mean μ by at least k standard deviations is given by:
P(|X - μ| ≥ kσ) ≤ 1/k^2
In our case, we want to find the upper bound for P[A ≥ 30]. Using Chebyshev's inequality, we can set k = (|30 - μ|)/σ and find an upper bound for the probability:
k = (|30 - 15|) / sqrt(10.5) ≈ 2.89
Therefore, according to Chebyshev's inequality:
P[A ≥ 30] ≤ 1/2.89^2 ≈ 0.122
Markov's Inequality:
Markov's inequality provides an upper bound on the probability of a random variable exceeding a specific value by a positive factor:
P(X ≥ a) ≤ E(X) / a
In our case, we want to find the upper bound for P[A ≥ 30]. Using Markov's inequality, we have:
P[A ≥ 30] ≤ E(A) / 30
Since E(A) = μ = 15:
P[A ≥ 30] ≤ 15 / 30 = 0.5
Therefore, according to Markov's inequality:
P[A ≥ 30] ≤ 0.5
In summary, these inequalities provide bounds on the probability of obtaining at least 30 heads when flipping the biased quarter 50 times.
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Related Questions
Please help me out and check the question !! ...
Answers
Because for each minute it goes up 200 more.
Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 = 36, z = 4
Answers
The set of points whose coordinates satisfy the conditions x² + y² + z² = 36 and z = 4 is a circle in the plane z = 4 with radius 2√5.
The equation x² + y² + z² = 36 represents a sphere centered at the origin with radius 6. Since the equation z = 4 is given, we know that the points in question lie on a plane parallel to the xy-plane at a distance of 4 units above it. Therefore, we can think of this problem as finding the intersection of the sphere and the plane z = 4.
To find the intersection, we can substitute z = 4 into the equation of the sphere:
x² + y² + 4² = 36
x² + y² = 20
This is the equation of a circle in the xy-plane with center at the origin and radius 2√5. Therefore, the set of points whose coordinates satisfy the given conditions is a circle in the plane z = 4 with radius 2√5.
Therefore, the set of points whose coordinates satisfy x² + y² + z² = 36 and z = 4 is a circle in the plane z = 4 with radius 2√5.
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Find the area of the isosceles triangle.
17 cm
16 cm
using pythagoras
Answers
Answer:
17cm
Step-by-step explanation:
The equation of the line that passes through points (0, negative 7) and (2, negative 1) is shown below. What value is missing from the equation?
y = x – 7
Answers
Answer:
answer is y= -3x-7
Step-by-step explanation:
Answer:
3x-7
Step-by-step explanation:
The radius of Mars is about 3.4 times 10^3 km. What is the approximate surface area of Mars? Use the formula for the surface area of a sphere, S.A.=4pieR^2. Write your answer in scientific notation
Answers
Answer: the answer is a hard doosie
Step-by-step explanation:
Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams, with the following results: Mean Grade Standard Deviation Professor 1 79.3 22.4 Professor 2 82.1 12.0 At the 2% level of significance, what is the decision
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Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.
In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.
In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.
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graph a line that contains the point (3,-6) and has slope of -1/2
Answers
Answer:
Step-by-step explanation:
Let the equation of the line is,
y = mx + b
Here, m = slope of the line
b = y intercept
Since, m = -\(\frac{1}{2}\)
Equation of the line will be,
y = \(-\frac{1}{2}x+b\)
Since, a point (3, -6) lies on the line,
-6 = \(-\frac{3}{2}+b\)
b = -6 + 1.5
b = -4.5
Equation of the line will be,
\(y=-\frac{x}{2}-\frac{9}{2}\)
Table for the points on the graph,
x -4 -3 -2 -1 0
y -2.5 -3 -3.5 -4 -4.5
Plot these points and join them to get the graph of a line.
Solve the equation 3.x + 5y= 15 for y.Not the correct equation
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We are given the following equation
\(3x+5y=15\)We are asked to solve the equation for y.
Solving for y means that we have to separate the variable y.
Step 1:
Subtract 3x from both sides of the equation
\(undefined\)15 points! Acellus pls help!:)
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Using the formula for lines intersecting & tangent to each other in a circle, we get the value of x to be = 6cm.
What are lines inside circle?A diameter is a line segment that traverses a circle by going through its centre.
The radius is twice as long as the diameter. A chord is a segment that does not have to pass through the centre and has endpoints on the circle.
We know that in a circle when lines are tangent and intersecting each other than the lines divided are in the formula:
a × b = c × d
Here,
x × a = 6 × 8
x = 6cm.
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Help pleaseeeee????????????
Answers
Answer:
y = 107 z = 73 x = 73
Step-by-step explanation:
Y and 107 are the same angle 107 + 73 = 180
How many real solutions does the quadratic equation below have?
y = 2? + 5x + 10
Answers
Answer:
their are 2
Step-by-step explanation:
A group of 42 children all play tennis or football, or both sports. The same number play tennis as play just football. Twice as many play both tennis and football as play just tennis. How many of the children play football?
Answers
Answer:
10.5 children play football
Step-by-step explanation:
10.5+10.5+21=42
Answer: 35 children
Step-by-step explanation:
Let the number of children who play only football be f , the number of children who play only
tennis be t and the number of children who play both sports be b.
Since there are 42 children, f + t + b = 42.
Also, since the number of children who play tennis is equal to the number of children who play
only football, t + b = f . Therefore f + f = 42. So f = 21 and t + b = 21.
Finally, twice as many play both tennis and football as play just tennis. Therefore b = 2t.
Substituting for b, gives t + 2t = 21. Hence t = 7.
Therefore the number of children who play football is 42 − t = 42 − 7 = 35.
How can we change 1 litre into 1000cm3
Answers
To change from litres into cubic centimetres, you times the value by 1000.
Eg:
Imagine the question “turn 5 litres into cm³”
First step would be to figure out how many litres we have, which is 5.
Now, we multiply 5 by 1000, which gives us 5000.
Therefore 5 litres = 5000cm³
I hope this helps and made sense, if you have any more questions or need me to explain further, just ask! :)
(If I helped you at all I’d greatly appreciate a thanks or if I really helped you a Brainliest!)
Step-by-step explanation:
1 Liter (L) is equal to 1000 cubic centimeters (cm3). To convert liters to cubic centimeters, multiply the liter value by 1000. For example, to convert 2 liters to cubic centimeters, multiply 2 by 1000, that makes 2 L is 2000 cm3.
Use a calculator to determine the measure of 0, in degrees, given that Csc (0) = 1.7894
Answers
If Csc(θ) = 1.7894 then θ = 34°.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
Csc(θ) = 1.7894
To find the value of θ:
θ = Csc⁻¹(1.7894)
By the Cosecant calculator,
θ = 34°
Therefore, the value of θ = 34°.
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Is the ordered pair (4, 16) a solution to this equation? y = 3 x 4; (4, 16) True or False
Answers
Answer:
True
Step-by-step explanation:
I'm assuming you mean y=3x+4.
First, in order to know if the point is a solution to the equation, all you have to do is to plug in the points and see if they are true.
\(y=3x+4; (4, 16)\)
16=3(4)+4
16=12+4
16=16
the solution is true!
In a family with 7 children, excluding multiple births, what is the probability of having 7 boys? Assume that a girl is as likely as a boy at each birth. Let E be the event that the family has 7 boys, where the sample space S is the set of all possible permutations of girls and boys for 7 children. Find the number of elements in event E, n(E), and the total number of outcomes in the sample space, n(S). n(E) = n(S)=
Answers
The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.
To find the probability, we need to calculate n(E) and n(S).
In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.
This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.
Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.
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55 = 18 +0.004x
What is x
Answers
37=0.004x
9250=x
Answer:
Your answer is: x = 9250
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Hope this helped : )
given a set x, the relation of equipotence is an equivalence relation on the collection 2x of all subsets of x. the equivalence class of a set with respect to the relation equipotence is called the cardinality of the set.
Answers
The relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.
The relation of equipotence is an **equivalence relation** on the collection 2x, which represents all subsets of set x. The equivalence class of a set, with respect to the relation of equipotence, is known as the **cardinality** of the set.
An equivalence relation is a relation on a set that satisfies three properties: reflexivity, symmetry, and transitivity. Let's explore how the relation of equipotence satisfies these properties.
1. Reflexivity: For any set A in 2x, A is equipotent to itself. In other words, any set is equivalent to itself in terms of its cardinality. This satisfies the reflexivity property of an equivalence relation.
2. Symmetry: If set A is equipotent to set B, then set B is equipotent to set A. The notion of equipotence does not depend on the order or arrangement of elements within sets. So, if A has the same cardinality as B, then B also has the same cardinality as A. This satisfies the symmetry property.
3. Transitivity: If set A is equipotent to set B, and set B is equipotent to set C, then set A is equipotent to set C. If two sets have the same cardinality and one of them has the same cardinality as a third set, then the first set is also equipotent to the third set. This satisfies the transitivity property.
As a result, the relation of equipotence on 2x fulfills all the requirements of an equivalence relation. Each equivalence class, or set of sets, formed by this relation represents the sets that share the same cardinality.
The cardinality of a set is essentially a measure of the "size" or "number of elements" in that set. It is represented by a non-negative integer. For example, if set A has three elements, its cardinality is 3. The equivalence class of set A, with respect to the relation of equipotence, would consist of all sets that have the same cardinality as A, that is, all sets with three elements.
In summary, the relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.
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The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. 115 182 255 419 442 461 517 739 743 789 807 865 925 984 1026 1063 1064 1165 1191 1222 1222 1252 1277 1290 1358 1369 1409 1455 1479 1519 1578 1578 1599 1604 1605 1696 1736 1799 1815 1853 1899 1926 1966
(a) Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution?
(b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean=1191.6, s=506.6.]
Answers
(a) Yes, a confidence interval for the true average lifetime can be calculated without assuming anything about the nature of the lifetime distribution.
(b) Using the given data, we can calculate a confidence interval with a 99% confidence level for the true average lifetime, with a mean of 1191.6 and a standard deviation of 506.6.
(a) It is possible to calculate a confidence interval for the true average lifetime without assuming any specific distribution. This can be done using methods such as the t-distribution or bootstrap resampling. These techniques do not require assumptions about the underlying distribution and provide a reliable estimate of the confidence interval.
(b) To calculate a confidence interval with a 99% confidence level for the true average lifetime, we can use the sample mean (1191.6) and the sample standard deviation (506.6). The formula for calculating the confidence interval is:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
The critical value depends on the desired confidence level and the sample size. For a 99% confidence level, the critical value can be obtained from the t-distribution table or statistical software.
The standard error is calculated as the sample standard deviation divided by the square root of the sample size.
Once we have the critical value and the standard error, we can calculate the confidence interval by adding and subtracting the product of the critical value and the standard error from the sample mean.
Interpreting the confidence interval means that we are 99% confident that the true average lifetime falls within the calculated range. In this case, the confidence interval provides a range of values within which we can expect the true average lifetime of individuals suffering from blood cancer to lie with 99% confidence.
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find the percentage profit in each case cost price 20 selling price 25
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
for profit percentage
p% =(sp-cp/cp)×100%
=(25-20/20)×100%
=25%
The profit percentage is 25%
Christian is conducting a survey to find out what technology device is the most popular. He wants to make sure his question is relevant to his topic. What question should Christian ask on his survey? (2 points) How many hours do you spend on technology every day? What do you use your technology devices for? Do you have a technology device? What technology devices do you use every day?
Answers
Answer:
What technology devices do you use everyday?
Step-by-step explanation:
Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.
Answer:
What technology devices do you use everyday?
Step-by-step explanation:
Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.
What is -2(3x - 9) + 5x = -10
Answers
Answer:
x=28
Step-by-step explanation:
-2(3x-9)+5x =-10
now we times -2 to to the inside of the parenthese
giving us
-6x+18 +5x= -10
add like terms
add -6x and 5x
-1x+18=-10
now we add like terms of the constants
minus 18 on both sides
-1x=-28
now divide by -1
x = 28
Answer:
x = 28
Step-by-step explanation:
First, remove the parentheses by distributing -2.
-6x + 18 + 5x = 10
Next, collect the like terms.
-x + 18 = -10
Next, move the constant to the right-hand side and change its sign.
-x = -10 - 18
Next, calculate the difference
-x = -28
Lastly, change the signs on both sides of the equation.
x = 28
These are the steps to answer this equation.
This is a project that’s half my grade please if you can give me the answer to all of them . I’m giving 50 points
Answers
Answer:
I can see how many guests that are there
I would still like to help though!
A radio is on sale for half price. Let y be its original price. Write an expression that tells its sale price.
Answers
Answer:
50% off of y
Step-by-step explanation:
This is hard I need help
Answers
Answer:
140.22 ft²Step-by-step explanation:
Surface area is the sum of areas of 4 triangles.
Each triangle has:
b = 9 ft, h = 7.79 ftArea of each triangle:
A = 1/2bhA = 1/2*9*7.79 = 35.055 ft²Surface area:
S = 4*35.055 = 140.22 ft²pls help i need it . A linear function contains the following points. What are the slope and y-intersept of this function?
Answers
Answer:
A
Step-by-step explanation:
We will use the formula for finding slope rise/run = y2 - y1/x2 - x1
6 - 8/0 - -2 = -2/2 = -1
And for the y-intercept, if x is 0 on that point, the y value is the y-intercept.
On this table, when x was 0, y was 6. So 6 is the y-intercept.
Slope is -1
y intercept is (0,6)
=============================================
Explanation:
Let's start with the slope. We'll use the aptly named slope formula.
Each row in the table represents a different (x,y) point.
\((x_1,y_1) = (-2,8) \text{ and } (x_2,y_2) = (0,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 8}{0 - (-2)}\\\\m = \frac{6 - 8}{0 + 2}\\\\m = \frac{-2}{2}\\\\m = -1\\\\\)
The slope is -1. This means the answer is between choice A or choice B.
----------------
The y intercept is very easy to spot for this particular table.
The y intercept always has x = 0. From the table, we see that x = 0 in the second row which points to 6 being the y intercept. More specifically, the location of the y intercept is (0,6)
This means we can rule out choice B and go for choice A as the final answer.
keiko tosses one penny and ephraim tosses two pennies. what is the probability that ephraim gets the same number of heads that keiko gets? express your answer as a common fraction.
Answers
The probability that Ephraim gets the same number of heads that Keiko gets is 3/8.
What is probability?
The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.
Here, we
Let K(n) be the probability that Keiko gets n heads, and let E(n) be the probability that Ephriam gets n heads.
K(0) = 1/2
K(1) =1/2
K(2) = 0 (Keiko only has one penny!)
E(0) = 1/2 ×1/2 = 1/4
E(1) = 1/2 ×1/2 + 1/2 ×1/2 = 1/2 (because Ephraim can get HT or TH)
E(2) = 1/2 ×1/2 = 1/4
The probability that Keiko gets 0 heads and Ephriam gets 0 heads is K(0)×E(0). Similarly for 1 head and 2 heads.
We get
P = K(0)× E(0) + K(1)×E(1) + K(2)× E(2)
P = 1/2 ×1/4 + 1/2 ×1/2 +0
P = 3/8
Hence, the probability that Ephraim gets the same number of heads that Keiko gets is 3/8.
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If l \\ m, find the value of x and y
Answers
Answer:
x is a horizontal line and y is a vertical line
a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 411.0 gram setting. it is believed that the machine is underfilling the bags. a 35 bag sample had a mean of 406.0 grams. a level of significance of 0.05 will be used. state the hypotheses. assume the standard deviation is known to be 25.0.
Answers
Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.
To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.
Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)
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. a bookstore owner estimates that her weekly profi ts p can be described by the equation p 5 8b 2 560, where b is the number of books sold that week. last week the store’s profi t was $720. what is the number of books sold?
Answers
The number of books sold last week by the bookstore owner is 10.Based on the given equation and the profit of $720 from last week, the number of books sold by the bookstore owner is estimated to be 10.
Given the equation p = 8b^2 + 560, where p represents the weekly profit and b represents the number of books sold, we can substitute p = 720 (the profit from last week) into the equation:
720 = 8b^2 + 560
Rearranging the equation, we have:
8b^2 = 720 - 560
8b^2 = 160
Dividing both sides of the equation by 8, we get:
b^2 = 20
Taking the square root of both sides, we find:
b = ±√20
Since b represents the number of books sold, we consider only the positive value, which is approximately 4.47. However, since the number of books sold must be a whole number, the closest integer value is 4.
Therefore, the number of books sold last week by the bookstore owner is 10.Based on the given equation and the profit of $720 from last week, the number of books sold by the bookstore owner is estimated to be 10.
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