Probability and statistics
The median of a random variable X to a continuous probability distribution is a
constant m such that P(X ≤m) = 1/2
Find the median of a random variable having pdf f(x) = 3x−4 for x ≥1 (and 0
otherwise).
Answers
The median of the random variable X with pdf f(x) = 3x−4 for x ≥1 (and 0 is approximately 1.482.
To find the median of a random variable with the given probability density function (pdf) f(x) = 3x - 4 for x ≥ 1 (and 0 otherwise), we need to solve for the constant m such that the cumulative probability P(X ≤ m) = 1/2.
First, we find the cumulative distribution function (CDF) by integrating the pdf:
F(x) = ∫(3x - 4) dx, where the limits of integration are from 1 to x.
F(x) = [(3/2)x² - 4x] evaluated from 1 to x.
Now, set the CDF equal to 1/2 to find the median:
1/2 = [(3/2)m² - 4m] - [(3/2)(1)² - 4(1)]
1/2 = (3/2)m² - 4m - (1/2)
1 = 3m² - 8m
0 = 3m² - 8m - 1
To find the value of m, we solve the quadratic equation above. Unfortunately, it cannot be factored easily, so we use the quadratic formula:
m = (-b ± √(b² - 4ac)) / 2a
In this case, a = 3, b = -8, and c = -1. Plugging in these values:
m ≈ (8 ± √(64 + 12)) / 6 ≈ 1.482
Since the median must be greater than or equal to 1, we take the positive root of the equation: m ≈ 1.482. Thus, the median of the random variable X with the given pdf is approximately 1.482.
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Related Questions
A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps
Answers
The standard form of a hyperbola with center (h,k) is
We know the vertices are at (5,0) and (-5,0)
The vertices are at (h+a,k) and ( h-a,k)
The center must be at (0,0) and the a value is 5
The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)
c is equal to 6
We know that c^2 = a^2+b^2
6^2 = 5^2 + b^2
36 = 25+b^2
11 = b^2
We can write the equation
Wendy and her friend Sandra went to dinner. Their total food bill was $25.00. The tax was 7%. How much was the tax? How much was the bill including the tax?
Answers
Answer:
the answer is 175
Step-by-step explanation:
you will do 2500*7/100
How do you find the missing length of an obtuse triangle?
Answers
To find the missing length of an obtuse triangle, use the Law of Cosines to calculate the length using the lengths of the other two sides and the angle opposite the missing side.
To find the missing length of an obtuse triangle, you can use the Law of Cosines. This law states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those sides and the cosine of the angle between them. In the case of an obtuse triangle, the angle opposite the missing side is greater than 90 degrees. To use the Law of Cosines to calculate the missing length, you will need to know the lengths of the other two sides and the angle opposite the missing side. Plug these values into the equation, and solve for the length of the missing side. This will then give you the missing length of the obtuse triangle.
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Mr. Titus travels from Charlotte to New York City and back 12 times each year. The total distance for each round trip is 623 miles. What is the total number of miles Mr. Titus travels from Charlotte to New York City and back each year? Enter your answer in the box.
Answers
Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.
The total distance will be calculated as:-
Distance = 12 x 623
Distance = 7476 miles
Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.
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Isaac walks 6/10 of a mile in 1/5 of an hour. If Isaac’s walking rate remains constant, what is Isaac’s walking rate in miles per hourur
Answers
Answer: 3 mph
Step-by-step explanation:
I did it in mah brain
A social networking site currently has 40,912 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 10 months?
Answers
Answer:
24496
Step-by-step explanation:
40912 * (1-5%) ^10 = 24495.5
becuase they are humans, so round up to 24496
Which is a solution to the system of inequalities? y > - 2x + 5 ; 3x - 4y ≤ - 24
Answers
Answer:
y > 2x+5 and y > 6+ 3z/4
Step-by-step explanation:
solve each inequality and then find the intersection
Answer:
y > - 2x
Step-by-step explanation:
April is going to the bakery to purchase donuts and cinnamon rolls for the office personnel. She must purchase at least 30 items. She has collected only $30, so total cost must be no more than $30. If d represents donuts that cost $0.75 each and r represents cinnamon rolls that cost $1.25 each, which system of inequalities can be used to represent the region for the number of donuts and cinnamon rolls April could purchase
Answers
Answer:
d + r ≥ 30
$0.75d + $1.25r ≤ $30
Step-by-step explanation:
Given the following :
Number of items to purchase = atleast 30
Total cost must be no more than 30
cost of donut (d) = $0.75
Cost of cinnamon (r) = $1.25
Number of donuts and cinnamon to purchase
To total number of items :
Donut + cinnamon ≥ 30
d + r ≥ 30
Cost of items to purchase :
Cost = price per item * number of items
$0.75d + $1.25r ≤ $30
imagine you are performing a two-way anova test, and you find a p-value for interaction of 0.07. what is the correct interpretation of this p-value with an alpha level of 0.05?
Answers
The correct interpretation of this p-value with an alpha level of 0.05 is explain below.
What is the correct interpretation of this p-value with an alpha level of 0.05?P-value is the margin of error importance inside a factual speculation test, addressing the likelihood of the event of a given occasion.
According to question:We have, P-value =0.07
Level of significance = 0.05
We know that,
P-value is less than level of significance, then H® is rejected,smaller the p-value longer the evidence that you should reject the null hypothesis.
Now P-value is greater than 0.05.
With a p-value greater than 0.05, fail to reject the H®.Look at multiple comparison of each Level of significance.
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18 ft
Talisa plans a 36-foot deep pond. While digging, she hits rock 30 feet down.
How can Talisa modify the radius to maintain the orginal volume of the
pond?
30 ft
36 ft
pond
pond
dirt
Answers
To maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129.
If Talisa hits rock at 30 feet, then the depth of the pond will be limited to 30 feet. Therefore, she needs to modify the radius of the pond to maintain the original volume.
To do this, Talisa can use the formula for the volume of a circular cylinder, which is:
V = πr^2h
where V is the volume of the cylinder, r is the radius, and h is the height (or depth) of the cylinder.
Since Talisa wants to maintain the original volume of the pond, she can set the equation for the new cylinder equal to the equation for the original cylinder, and solve for the new radius, r2:
πr1^2h1 = πr2^2h2
where r1 is the original radius (unknown), h1 is the original height (36 ft), r2 is the new radius (unknown), and h2 is the new height (30 ft).
Simplifying this equation, we can cancel out the π and h1 terms:
r1^2 = r2^2(30/36)
Taking the square root of both sides, we get:
r1 = r2(√(30/36))
Thus, to maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129. In other words, she needs to multiply the original radius by 0.9129 to get the new radius.
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HURRYYYY Are these expressions equivalent? Explain why or why
not.
42 + 35
7(6 + 5)
Answers
Answer:
Yes, they are equivalent!
Step-by-step explanation:
42+35=77
PEMDAS calls for 6+5 ( in parentheses ) which equals 11.
11*7=77
Answer:
equivalent
Step-by-step explanation:
42+35=77
7(6+5)=42+35
which is 77
and 77=77
formula of amount when interest and principal is given
Answers
Answer:
We can rearrange the interest formula, I = PRT to calculate the principal amount. The new, rearranged formula would be P = I / (RT), which is principal amount equals interest divided by interest rate times the amount of time.
Step-by-step explanation:
Hope this helps you sorry if it does not help you
State whether the following categorical propositions are of the form A, I, E, or O. Identify the subject class and the predicate class. (1) Some cats like turkey. (2) There are burglars coming in the window. (3) Everyone will be robbed.
Answers
Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.
The given categorical propositions and their forms are as follows:
(1) Some cats like turkey - Form: I:
Subject class: Cats,
Predicate class: Turkey
(2) There are burglars coming in the window - Form: E:
Subject class: Burglars,
Predicate class: Not coming in the window
(3) Everyone will be robbed - Form: A:
Subject class: Everyone,
Predicate class: Being robbed
In the first statement:
Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.
In the second statement:
There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.
In the third statement:
Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.
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SOMEONE PLEASE HELP ME...
If k=
\( log_{2}(3) \)
Rewrite
\( log_{2}(48) \)
in terms of k.
Answers
9514 1404 393
Answer:
k+4
Step-by-step explanation:
48 = 16×3 = 2^4×3
log2(48) = log2(2^4) +log2(3)
log2(48) = 4 + k
Which of the following statements is true about lines
Answers
solve the two-step equation. -1/3x-21/4=27/4
Answers
Answer:
x=(-36)
Step-by-step explanation:
Answer:
x = -36.
Step-by-step explanation:
-1/3x-21/4=27/4
-1/3x = 27/4 + 21/4
-1/3x = 48/4 = 12
x = 12* -3
x = -36.
how do I solve this? 9 3/10 - 2 7/10
Answers
EXPLANATION
The expression 9 3/10 first you be converted into a improper fraction as follows:
9 3/10 = 93/10
Applying the same operation for 2 7/10:
2 7/10 = 27/10
Then, subtracting both fractions:
93/10 - 27/10 = 66/10
Simplifying the fraction:
33/5
The answer is 33/5
The diagram below shows the graph of h(t), which models the height, in feet, of a rocket t seconds after it was shot into the air 
Answers
The domain is the set of all t-value (inputs) used by the function/graph.
The least t-value is 0. The greatest is 4.
The domain is [0,4].
The domain of graph for function h(t) is [0,4].
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values of a function like f(x) are part of this collection. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
a diagram below shows the graph of h(t), which models the height in t seconds.
we know that the domain are the input values.
Here the domain is the set of all t-value used in the graph.
So, from the graph we can see that the least t-value is 0 and the greatest is 4.
Thus, the domain of graph is [0,4].
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people taking part in an experiment are called variables.
Answers
Answer:
Yes, people that taking part in an experiment are called variables.
There is normally one person called the dependent variable, and the other who is the independent variable.
The statement provided "people taking part in an experiment are called variables" is incorrect.
In an experiment, the individuals or subjects who participate and are observed or manipulated are not referred to as variables. Instead, they are called participants, subjects, or sometimes, respondents, depending on the context of the study.
Variables, on the other hand, are characteristics or properties that can vary or change among the individuals or subjects in the study. Variables can be classified as independent variables, dependent variables, or control variables.
Independent variables are manipulated or controlled by the researcher, while dependent variables are the outcomes or responses that are measured or observed.
Control variables are other factors that are held constant. Therefore, it is important to differentiate between the individuals participating in the experiment and the variables being studied.
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A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)
(a)
Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic. (Round your answer to two decimal places.)
Answers
The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.
Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:
p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.
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Which expression is the same as 15 of 8?
8÷5
5÷8
5×8
1/5×1/8
Answers
Help me, 50 pts, I'll give brainliest, *take your time answering if you need *
1. how many groups of 5/7 are in 1
2. 8 divided by 5/7
3. The tape diagram shows that Ehecatl's hair, which is now 12cm long is 60% as long as it was before his haircut.
Complete the table to show different percentages of Ehecatl's hair length before the haircut. (table is the file)
Answers
There are 1.40 groups of 5/7 in 1.
8 divided by 5/7 is 11 1/5.
Here is the completed table:
Length (cm) Percentage
12 60% of Ehecatl's old hair
4 20% of Ehecatl's old hair
20 100% of Ehecatl's old hair
How do we carry out division?Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine how many groups of 5/7 are in 1, divide 1 by 5/7
1 ÷ 5/7
1 x 7/5 = 7/5 = 1.40
8 ÷ 5/7
8 x 7/5
= 56 / 5
= 11 1/5
What are the lengths of Ehecatl's hair ?
The first step is to determine the length of her hair before she cut it
Length of the hair before it was cut = new length / 60%
12 / 0.6 = 20
60% x 20 = 12cm
20% x 20 = 4cm
100% x 20 = 20cm
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What is value of x in the equation below? 33 ≥ -6x + 9
Answers
Answer:
x ≥ -4
or [-4, ∞)
Step-by-step explanation:
What is value of x in the equation below?
33 ≥ -6x + 9
subtract 9 from both sides:
33 - 9 ≥ -6x + 9 - 9
24 ≥ -6x
divide both sides by -6 and remember to flip sign direction:
24/-6 ≥ -6x/-6
-4 ≤ x
or: x ≥ -4
in set builder notation: [-4, ∞)
Answer:
Below in bold
Step-by-step explanation:
33 ≥ -6x + 9
-6x ≤ 33 - 9
-6x ≤ 24
x ≥ -4
- note that the inequality is flipped as we are dividing by a negative.
change 6 to percentage.
-
25
Answers
Answer:
24%
Step-by-step explanation:
6÷25×100
to find in percentage
Answer:
6 as a percent would be 0.06.
Step-by-step explanation:
100 as a percent is 1.00
90 as a percent is 0.90
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Try It Another Way Work with your group to predict whether each equation is
a linear function. Then graph each equation on a separate sheet of paper. Describe
the results.
7 y = 0.5x + 2
8 y = 0.5x³
Answers
Because y = 0.5x + 2 is a first-degree polynomial with 1 as the highest power, it is a linear function. We obtain a straight line when we graph it.
what is linear function ?In mathematics, a linear function is a particular kind of function where the rate of change between the input (an independent variable) and the output is constant (dependent variable). In other words, when graphed on a coordinate plane, a linear function displays a straight line. A linear function's generic form is: y = mx + b where x is the independent variable, y is the dependant variable, b is the y-intercept (the point where the line crosses the y-axis), and m is the slope of the line (the rate of change). A linear function's slope, also known as rise over run, is defined as the change in y divided by the change in x.
given
Because y = 0.5x + 2 is a first-degree polynomial with 1 as the highest power, it is a linear function. We obtain a straight line when we graph it.
Because \(y = 0.5x^{3}/8\) is a third-degree polynomial with 3 as the maximum power of the variable x, it is not a linear function. We get a curve instead of a straight line when we graph it.
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Ike Phillips worked 6.7 hours at time-and-a-half pay and 3.4
hours at double-time pay last week. His regular earnings for
the week were $454.80 figured on a regular pay rate of $11.37
an hour.
27. What were Ike's time-and-a-half and double-time pay rates?
28. What amounts did he earn for time-and-a-half and double-time work?
29. What was Ike's total gross pay for the week?
Answers
Working out the different pay rates earned by Ike Phillips :
Time and half pay rate = $17.055Double pay rate = $22.74Time and half earning = $114.2685Double rate earning = $77.316Gross earning = $646.3845Let :
Regular rate = $11.37
Total earning for the week = $454.80
Double pay hours = 3.4
Time and half pay hours = 6.7
Time and half pay rate = 1.5 × regular pay rate = 1.5 × 11.37 = $17.055Double pay rate = 2 × regular pay rate = 2 × 11.37 = $22.74Time and half earning = rate × time = $17.055 × 6.7 = $114.2685 Double rate earning = rate × time = $22.74 × 3.4 = $77.316Gross earning = (regular + time and half + double earning) = $(454.80+114.2685+77.316) = $646.3845Therefore, Ike's gross earning for the week is $646.3845
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Does anybody know how to solve this? I really need help.
Answers
Answer:
83
Step-by-step explanation:
When the altitude of a triangle is the perpendicular bisector of the base, that triangle is isosceles. That means QM = SM, which is a relation that lets us find the value of x.
QM = SM
3x +10 = 5x -2
12 = 2x . . . . add 2-3x to both sides
6 = x
The sum of the side lengths is ...
P = QM +SM +QS
P = (3x+10) +(5x -2) +(4x +3) = 12x +11
For x=6, this is ...
P = 12(6) +11 = 72 +11 = 83
The perimeter of the triangle is 83 units.
Need help for question number 1
Answers
Answer:
I believe that the answer is a
Step-by-step explanation:
tangent is
opposite/adjacent
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 4 m/s?. If the same force acts upon another object whose mass is 2 kg, what is this object's acceleration?
Answers
Answer:
14 m/s²
Step-by-step explanation:
From the question
a ∝ F/m.............. Equation 1
Where a = aceleration, m = mass, F = force
make F the subject of the equation
F = ma............ equation 2
Given: m = 7 kg, a = 4 m/s²
Therefore,
F = 7(4)
F = 28 N
For another object whose mass is 2 kg,
Make a the subject of equation 2
a = F/m
a = 28/2
a = 14 m/s²
Help with congruent angles - please----
State if the 2 angles are congruent.
If they are, state how you know- for example SSS or SAS.
Answers
Answer:
SAS TRIANGLESStep-by-step explanation:
the triangles have two equal sides
and one angle