Homework Answers
Add Answer to:
(20 pts) Suppose that Xi,X2 X3, X4 are independent random variables, all of which have mean...
(20 pts) Suppose that 1, 2, X3, X4 are independent random variables, all of which have...
(20 pts) Suppose that 1, 2, X3, X4 are independent random variables, all of which have mean μ and variance σ2 (a) Yi = 0.25x1 + 0.25x2+ 0.25x3 + 0.25x4 (b) ½ = 0.1X1 + 0.2X2 + 0.3X3 + 0.4X4 (c) YS = 0.5X1 + 0.4X2 + 0.3X3-0.2X1 What do you observe about the expectation of Y ,½,⅓? Which of these random variables has the LEAST variance?
Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y;...
Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y; be the partial sums, i.e., Y1 = X1, Y2 = X1 + X2, Y3 = X1 + X2 + X3. 1. What is the distubution for each Yį, i = 1, 2, 3? 2. What is the expected value for Y1 + Y2 +Yz? 3. Are Yį and Y2 independent? Explain it by computing their joint P.M.F. 4. What is the variance of Y1...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the joint probability that all Xi, (i-1,.5), are larger than 9.
Suppose we have 5 independent and identically distributed random variables Xi,X2.X3,X4,X5 each with the moment generating...
Suppose we have 5 independent and identically distributed random variables Xi,X2.X3,X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y -XX. The density function of Y is (a) Poisson with λ-40 (b) Gamma with α-10 and λ-8 (c) Normal with μ-40 and σ-3.162 (d) Exponential with λ = 50 (e) Normal with μ-50 and σ2-15
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3).
3. (25 pts.) Let X1,...
4.5 The pdfs of two independent random variables Xi and X2 are e-*, for xi >...
4.5 The pdfs of two independent random variables Xi and X2 are e-*, for xi > 0; fx,(x) = for x2>0; for x2 fXy(x) = 0, 0. Determine the jpdf of Yi and Y2, defined by Yi and show that they are independent
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convol...
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1):
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1):
5. Suppose that Xi, X2, and X3 are independent random variables such that EX i12,3. Find...
5. Suppose that Xi, X2, and X3 are independent random variables such that EX i12,3. Find the value of ElX(2X1- X3)21. dEX? 1 for
Let x1, x2, x3, x4 be independent standard normal random variables. Show that , , are...
Let x1, x2, x3, x4
be independent standard normal random variables. Show that
,
,
are independent and each follows a
distribution
(x1 - r2)
(20 pts) Suppose that 1, 2, X3, X4 are independent random variables, all of which have mean μ and variance σ2 (a) Yi = 0.25x1 + 0.25x2+ 0.25x3 + 0.25x4 (b) ½ = 0.1X1 + 0.2X2 + 0.3X3 + 0.4X4 (c) YS = 0.5X1 + 0.4X2 + 0.3X3-0.2X1 What do you observe about the expectation of Y ,½,⅓? Which of these random variables has the LEAST variance?
Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y; be the partial sums, i.e., Y1 = X1, Y2 = X1 + X2, Y3 = X1 + X2 + X3. 1. What is the distubution for each Yį, i = 1, 2, 3? 2. What is the expected value for Y1 + Y2 +Yz? 3. Are Yį and Y2 independent? Explain it by computing their joint P.M.F. 4. What is the variance of Y1...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the joint probability that all Xi, (i-1,.5), are larger than 9.
Suppose we have 5 independent and identically distributed random variables Xi,X2.X3,X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y -XX. The density function of Y is (a) Poisson with λ-40 (b) Gamma with α-10 and λ-8 (c) Normal with μ-40 and σ-3.162 (d) Exponential with λ = 50 (e) Normal with μ-50 and σ2-15
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3).
3. (25 pts.) Let X1,...
4.5 The pdfs of two independent random variables Xi and X2 are e-*, for xi > 0; fx,(x) = for x2>0; for x2 fXy(x) = 0, 0. Determine the jpdf of Yi and Y2, defined by Yi and show that they are independent
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1):
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1):
5. Suppose that Xi, X2, and X3 are independent random variables such that EX i12,3. Find the value of ElX(2X1- X3)21. dEX? 1 for
Let x1, x2, x3, x4
be independent standard normal random variables. Show that
,
,
are independent and each follows a
distribution
(x1 - r2)
Most questions answered within 3 hours.
-
The Baldwin Company currently has the following balances on their
balance sheet:
Total
Liabilities
$69,309
Common...
asked 43 seconds ago -
A quiet town in Kansas has 10 people, all of whom have the same
preferences. There...
asked 6 minutes ago -
Summarize what an organization needs from a leader.
a. Analyze what might happen to an organization...
asked 8 minutes ago -
How would one critically evaluate an organizations marketing
strategies from the viewpoint of its consumers, as...
asked 7 minutes ago -
Given a standardized normal distribution (with μ = 0 and a σ =
1), what is...
asked 8 minutes ago -
Company XYZ know that replacement times for the quartz time
pieces it produces are normally distributed...
asked 22 minutes ago -
A) Write the acid-base reaction that occurs between Na2HPO4 and
NaOH
B) Write the possible reactions...
asked 36 minutes ago -
What advantages does the Natural Law Theory have in comparison
with the Divine Command Theory? Explain...
asked 42 minutes ago -
A diver comes off a board with arms straight up and legs
straight down, giving her...
asked 41 minutes ago -
Answer the following questions
In your own words, define each of these terms
- Branding, Packaging,...
asked 39 minutes ago -
Briefly discuss developments in the crude oil market and your
outlook, using the microeconomic concepts discussed...
asked 40 minutes ago -
Electrons are accelerated through potential difference of 12 V
and are bombarding the hydrogen atoms. To...
asked 44 minutes ago