Let 1,...,5 represent independent random variables, each with the following
density function
(x)= {3x2 0≤x ≤1
0 otherwise
What is the probability density function of =max {1,...,5}?
What is the cumulative distribution function of =max {1,...,5}?
What is the probability density function of =min {1,...,5}?
What is the cumulative distribution function of =min {1,...,5}?
Answers
The CDF of Z is the probability that Z is less than or equal to a given value z. This is equal to the complement of the probability that at least one random variable is less than z.
To find the probability density function (PDF) and cumulative distribution function (CDF) of the maximum and minimum of a set of random variables, we need to consider the order statistics.
Let X1, X2, X3, X4, X5 be the independent random variables with the given density function f(x):
f(x) = 3x^2 0 ≤ x ≤ 10
0 otherwise
1. Probability density function (PDF) of Y = max{X1, X2, X3, X4, X5}:
To find the PDF of the maximum, we need to determine the probability that all random variables are less than or equal to a given value y. This is equivalent to finding the complement of the probability that at least one random variable is greater than y.
The PDF of Y is given by:
fY(y) = 1 - P(X1 > y, X2 > y, X3 > y, X4 > y, X5 > y)
= 1 - P(X1 > y) * P(X2 > y) * P(X3 > y) * P(X4 > y) * P(X5 > y)
= 1 - (1 - F(y))^5
where F(y) is the cumulative distribution function (CDF) of X1 (and also X2, X3, X4, X5), which is the integral of the density function f(x) from 0 to y.
2. Cumulative distribution function (CDF) of Y = max{X1, X2, X3, X4, X5}:
The CDF of Y is the probability that Y is less than or equal to a given value y. This is equal to the complement of the probability that all random variables are greater than y.
The CDF of Y is given by:
FY(y) = P(Y ≤ y)
= 1 - P(Y > y)
= 1 - (1 - F(y))^5
where F(y) is the CDF of X1 (and also X2, X3, X4, X5).
3. Probability density function (PDF) of Z = min{X1, X2, X3, X4, X5}:
To find the PDF of the minimum, we need to determine the probability that all random variables are greater than or equal to a given value z.
The PDF of Z is given by:
fZ(z) = P(X1 ≥ z, X2 ≥ z, X3 ≥ z, X4 ≥ z, X5 ≥ z)
= P(X1 ≥ z) * P(X2 ≥ z) * P(X3 ≥ z) * P(X4 ≥ z) * P(X5 ≥ z)
= F(z)^5
where F(z) is the CDF of X1 (and also X2, X3, X4, X5).
4. Cumulative distribution function (CDF) of Z = min{X1, X2, X3, X4, X5}:
The CDF of Z is the probability that Z is less than or equal to a given value z. This is equal to the complement of the probability that at least one random variable is less than z.
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Related Questions
In the figure, line p || line q. Find the measure of each angle if m<8 = 115
Answers
Answer:
65, 65, 115
Step-by-step explanation:
Attached image
You drink 14 ounces
of water in 10 minutes.
How would
you express this
relationship as a unit
rate per minute?
Answers
Answer:
1.4 per minute
Step-by-step explanation:
10 minutes/10=1 min.
=14/10=1.4=
1.4 ounces per minute
Direct Relationship
Please help quadratic equation!! 20 points
Answers
Answer:
x=4,−2
Step-by-step explanation:
Because Step 1. Move all terms to one side.
{x}^{2}-2x-8=0
x
2
−2x−8=0
2 Factor {x}^{2}-2x-8x
2
−2x−8.
1 Ask: Which two numbers add up to -2−2 and multiply to -8−8?
-4−4 and 22
Step 2. Rewrite the expression using the above.
(x-4)(x+2)
(x−4)(x+2)
and going to;
(x-4)(x+2)=0
(x−4)(x+2)=0
And Step 3. Solve for xx.
1 Ask: When will (x-4)(x+2)(x−4)(x+2) equal zero?
When x-4=0x−4=0 or x+2=0x+2=0
2 Solve each of the 2 equations above.
x=4,-2
x=4,−2
x=4,-2
Our Answer is:
x=4,−2
I Hope It's Helps
Answer:
2 and -4
tso numbers when added gives -2 and 8 incase it's not clear enough.
(b) Work out the value of (2.4 x 10³) x (9.5 x 10³)
Give your answer in standard form.
Answers
Answer:
\(2.28*10^7\)
Step-by-step explanation:
\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)
Answer:
228,000
Step-by-step explanation:
(2.4x10^3) x (9.5x10^3)
(2.4x100) x (9.5x100)
240x950
228,000
Evaluate 6+ 4/a + 3/b then a=4 and b=3
Answers
Answer:
The answer would be 8.
Step-by-step explanation:
Here the given expression,
6 + 4/a + 3/b
By substituting a = 4 and b = 3 in the above expression,
We get,
6 + 4/4 + 3/3
= 6 + 1 + 1
= 8
Therefore, the value of the given expression would be 8.
Answer: 8
Step-by-step explanation: Plug in a =4 and b=3 into 6+4/a +b/3 6 + 4/4 + 3/3= 6 + 1 + 1= 8
please help with this.
Answers
Answer:
b
Step-by-step explanation:
Answer:
I think your answer is B.
Step-by-step explanation:
Not 100% sure though
421 divided by 18 as a mixed number
Answers
Answer:
The correct answer is in the image!
Step-by-step explanation:
Hope that helps!
\(\tt \large \red\leadsto\: \: \frac{421}{18} \: = \: 23 \times \frac{7}{8} \\ \)
Which of the following is an integer?
10.5
-9
XandY
1/2
Answers
Answer:
-9
Step-by-step explanation:
an integer is a whole number!
A researcher believes that women today weigh less than in previous years. To investigate this belief, he randomly samples 41 adult women and records their weights. The scores have a mean of 111 lb & and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs.(a) The obtained value of the appropriate statistic for testing H0 is.(b) The dl for determined t is.(c) Using α=0.01 the appropriate critical value.
Answers
The critical value of the appropriate statistic for testing the null hypothesis is -0.322.
First we must define the Null Hypothesis
H0: Miu >= 115
Ha: Miu < 115
The null hypothesis is that the population mean Miu of weights of women is greater or equal than the one of previous years, 115 lbs. We define the hypothesis so that, if we reject the Null Hypothesis H0, we will prove what we want, that weights of women are less.
As our sample is greater than 30 observations, we can use the Central Limit Theorem and uses a Z statistic to prove the hypothesis ( in contrary we must use a t - test). The z statistic is
Z = sample mean - H0 / Std Deviation sample
Z= 111-115 / 12.4 = -4/12.4 = -0.322
The Z to test against your critical Z is the Z value that accumulates a 0.01 of probability or -2.32
Hence the answer is The critical value of the appropriate statistic for testing the null hypothesis is -0.322.
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Match the missing parts of the triangle with their correct length or measure.
HINT: The ONLY right triangles we are given in this problem are ADB and BDC. Triangle ABC is NOT necessarily a right triangle.
Given:
DB=24
AD=32
AC=42
DC=10
BC=26
AB=40
Measure
Measure of
Find:
Measure
Measure
Measure
Measure
Measure
Answers
The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given that, in △BCD
BD = 24 m
DC = 10 m
BC = 26 m
△BCD is a right angle triangle.
The trigonometry ratio of sine is ratio of height to hypothenuse.
With respect to C, the height of △BCD is 24m and hypothenuse is 26m.
sin C = height/hypothenuse
sin C = 24/26
C = 67.38°
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Please help I need to get this done please help me
Answers
Answer:
4
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis.
At (0,4), you can see the purple line cross the y-axis, therefore it is the y-intercept.
Answer:
3/4
Step-by-step explanation:
Which system of linear equations has a solution of (2, 3)?
Answers
Answer:
i don't know
Step-by-step explanation:
(0)
Question 2 Consider the dynamic system described by Equation Q2. 85.16400 083.3770 0046.999 ⃗+ 0.079400 00.7030 001.07 ×10⃗+ 0.013600 03.1390 005.124 ×10⃗= 0 0 0 Equation Q2 (a) Calculate the spectral matrix, the undamped natural frequencies and damping ratios of the system in Equation Q2. Identify its fundamental frequency. (b) The following mode shape vectors have been used to diagonalise the equations of motion of the dynamical system presented in Equation Q2: f1 = [0.8076 1.0000 0.8039]T; f2 = [-0.9694 -0.1620 1.0000]T and f3 = [-0.5342 1.0000 -0.3523]T. Calculate the respective matrix of mass normalised mode shapes. (c) Using the mode superposition method, calculate the response of the system for the first physical coordinate y1 assuming the following initial conditions expressed in terms of the modal coordinates: the initial modal displacements are [0 0.5 0]T m and the initial modal velocities are [0 -3 0]T m/s.
Answers
The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be normalising the mode shape vectors f1, f2, and f3.
Part (a)
In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.
The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].
The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].
The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.
The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.
The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.
The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.
Part (b)
The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.
The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.
The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.
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Student A can solve 75% of problems, student B can solve 70%. What is the probability that A or B can solve a problem chosen at random?
Answers
The probability that student A or B can solve a problem chosen at random is 0.95.
Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.
Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:
P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:
P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525
Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925
Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).
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Graph of.... 3 3=0 Y axis Solve the equation oc²³²= 2xx - 3=0 graphically x-20-3=0 Let you² - 2c-3 when y=0 you can find oc OC -2-1 oc² 1 4 4 2244 O O O Scale x axis -3-3-3-3 1 2 345 T 4 9 16 25 -2 -4 -6 -8 -10 -3-3-3-3-3 5/01-310-3 10 15/12
Answers
The solution to the equation does not exist
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
2x - 3 = 0
2x - 3 = 3
Also from the question, we understand that the graph is given as
3 = 0
The above equation is false, and cannot be represented on a graph
This is so because 0 and 3 do not have the same value
Similarly, we have 2x - 3 = 0 and 2x - 3 = 3
By substitution, the equations becomes
0 = 3
Hence, the equation has no solution
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Complete question
Graph of 3=0
Solve the equation 2x - 3 = 0 and 2x - 3 = 3 graphically
ten chairs are evenly spaced around a round table and numbered clockwise from 11 through 1010. five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. how many seating arrangements are possible?
Answers
There are 345,600 possible seating arrangements with the given restrictions.
To find the number of possible seating arrangements, we need to consider the restrictions given in the question.
1. The chairs are numbered clockwise from 11 through 1010.
2. Five married couples are sitting in the chairs.
3. Men and women are to alternate.
4. No one can sit next to or across from their spouse.
Let's break down the steps to find the number of possible arrangements:
Step 1: Fix the position of the first person.
The first person can sit in any of the ten chairs, so there are ten options.
Step 2: Arrange the remaining four married couples.
Since men and women need to alternate, the second person can sit in any of the four remaining chairs of the opposite gender, giving us four options. The third person can sit in one of the three remaining chairs of the opposite gender, and so on. Therefore, the number of options for arranging the remaining four couples is 4! (4 factorial).
Step 3: Consider the number of ways to arrange the couples within each gender.
Within each gender, there are 5! (5 factorial) ways to arrange the couples.
Step 4: Multiply the number of options from each step.
To find the total number of seating arrangements, we multiply the number of options from each step:
Total arrangements = 10 * 4! * 5! * 5!
Step 5: Simplify the expression.
We can simplify 4! as 4 * 3 * 2 * 1 = 24, and 5! as 5 * 4 * 3 * 2 * 1 = 120. Therefore:
Total arrangements = 10 * 24 * 120 * 120
= 345,600.
There are 345,600 possible seating arrangements with the given restrictions.
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what is 892.42 rounded tents place
Answers
892.4
May Nilbin Be With You
(PLS HELP WILL MARK BRAINLIEST TO CORRECT ANSWER)
John leaves his house one morning to go to the store which is 16 middles dude my north. Suzie, his wife, leaves the house and drives to work, which is directly east of the store.John needs to drop off lunch for suzie because she forgot to pack a lunch today. If suzie has a 20 mile drive to work from home, how far must John drive to store to deliver her lunch?
Answers
Answer: 12 miles
Step-by-step explanation:
Combining negatively correlated assets having the same expected return results in a portfolio with ____ level of expected return and ____ level of risk. Select one: a. a higher; a lower b. the same; a lower c. the same; a higher d. a lower; a higher
Answers
Combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk.
When assets have a negative correlation, their returns tend to move in opposite directions. By combining these assets in a portfolio, their negative correlation offsets each other's risks to some extent. As a result, the overall risk of the portfolio is reduced.
However, the expected return of the portfolio remains the same as the individual assets, assuming they have the same expected return. This is because the negative correlation does not affect the average return of the assets, only their volatility. The diversification benefits provided by negatively correlated assets help to reduce the overall risk of the portfolio, making it less volatile than the individual assets.
Therefore, combining negatively correlated assets with the same expected return results in a portfolio with the same level of expected return but a lower level of risk. This is a desirable outcome for investors as it allows them to achieve a certain level of return while minimizing the overall risk in their investment portfolio.
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Please help! i need to pass this
Answers
The synthetic division is expressed as 9x³ - 24x² + 49x - 100/x + 2
How to determine the division
To carry out synthetic division, we take the following steps;
Check whether the polynomial is in the standard form.Write the coefficients in the dividend's place and write the zero of the linear factor in the divisor's place.Bring the first coefficient downMultiply it with the divisor and write it below the next coefficient.Add them and write the value below.From the information given, we have;
9x³ - 6x² + x - 2/x + 2
Then, we have the set up as;
9 -6 1 - 2
-2 -18 48 -98
9 -24 49 -100
9x³ - 24x² + 49x - 100/x + 2
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What is the total distance around the coop
Answers
The answer is 20 meters.
I need help on this assignment question
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of x is 0.0036
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1.7 x \(10^{8}\) / 12 = 5.1 x \(10^{4}\) / x
Multiply x on both sides.
(1.7 x \(10^{8}\))x / 12 = 5.1 x \(10^{4}\)
Multiply 12 on both sides.
(1.7 x \(10^{8}\))x = 12 x 5.1 x \(10^{4}\)
Divide 1.7 x \(10^{8}\) on both sides.
x = (12 x 5.1 x \(10^{4}\)) / (1.7 x \(10^{8}\))
x = 36 x \(10^{4 - 8}\)
x = 36 x \(10^{- 4}\)
x = 36/10000
x = 0.0036
Thus,
The value of x is 0.0036
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What is another name for Plane P below?
A.
plane B
B.
plane n
C.
plane ABC
D.
plane BAD
Answers
Answer:
is. there. a. picture
Step-by-step explanation:
Çok acil arkadaşlar lütfen
Answers
Answer:
Step-by-step explanation:
I need help I don’t know what to do!?
Answers
Answer:
The slope is 4/3x
Step-by-step explanation:
We can easily find the slope, by looking at the difference between each number on the table. We can see that the x values are rising in 3's, and the y values are rising in 4's. From that we can find the slope, 4/3x, since the slope rises up positive 4, and runs positive 3.
EDIT: forgot the x after the slope
The sum of the digits of a two-digit number is seventeen. The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. What is the original number?
Answers
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
Given that the sum of the digits is seventeen, we have the equation:
x + y = 17 (equation 1)
The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.
According to the given information, we have the equation:
10y + x = 5x + 30 (equation 2)
To solve the system of equations, we can substitute equation 1 into equation 2:
10(17 - x) + x = 5x + 30
Expanding and simplifying:
170 - 10x + x = 5x + 30
170 - 30 = 5x + 10x - x
140 = 14x
x = 10
Substituting the value of x back into equation 1:
10 + y = 17
y = 7
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
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Fifth-grade students plant a class garden. They plant 7 1/6 rows of tomatoes and 3 1/2 rows of carrots. How many fewer rows of carrots than rows of tomatoes do the students plant?
Answers
Answer:
3 2/3
Step-by-step explanation:
7 1/6 - 3 1/2= 3 2/3
the diagram below of triangle OPQ, R is the midpoint of OQ and S is the
point of PQ. If RS =-3x+38,
and OP = 4x -14, what is the mea
52
Answers
The measurement of the angle OP is 39
How to find the measure of OP?The given parameters that will help us to answer the question are
R is mid point of OQ
S is mid point of PQ
RS = 3x + 38
OP = 4x- 14
R is mid point of OQ and S is mid point of PQ;
By using mid point theorem
[1/2][OP] = RS
This implies that So,
[1/2][3x + 38] = [4x- 14]
[3x+38] = 2[4x- 14]
Opening the brackets we have
3x+38=8x-28
Collecting like terms
3x-8x=-28-38
-5x=-66
Making x the subject of the relation we have
x = -66 / -5
x = 13.2
Therefore RS = 3(13.2) + 38 = -11.4
OP = 4(13.2)- 14=38.8
Measurement of OP = 39 approximately
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Find the area of the figure below
Answers
Answer:
you can write 28.5
Step-by-step explanation:
calculate the squared you can find it
What is the value of "b" in the following quadratic? (Make sure the equation is in
standard form: ax2 + bx+c=0)
X^2 + 28 = -112
Answers
Answer:
b = -84
Step-by-step explanation:
x² + 28 = -112
x² - 84 = 0
ax² + bx + c = 0
1x² + 0x + (-84) = 0
a = 1; b = 0; c = -84
Answer: b = -84