A random variable Q has pdf ?q(q) = {
− 2 ≤ Q ≤ 2; 0 else} .
(1) Find ?[Q], and Var(Q).
(2) Let Z = Q2. Find ?z(Z).
(3) Find P{Q > 1}
(4) Find conditional PDF of Q given B= {Q > 1} i.e., find ?Q|?(Q).
Homework Answers
The PDF of random variable X and the conditionalPDF of random variable Y given X are...
The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x)...
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x) = to else where c is a positive constant. (a) (5%) Find c. (b) (5%) Find the CDF of X, Fx(x). (c) (5%) Find Prob{2<x<5} (d)(5%) Find E[X], and Var(X).
Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( )...
Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( ) ?? + 0.4, 0 ≤ ? ≤ 2 0, ??ℎ?????? a. Find the value C that makes fX(x) a valid PDF. (Hint: Draw the PDF to start.) b. Find and sketch the CDF, FX(x). c. Calculate P[X > 1] d. Let A be the event that X > 1. Find and sketch the conditional PDF fX|A(x|A).
A continuous random variable Z is said to have a Laplace(H, b) distribution if its PDF...
A continuous random variable Z is said to have a Laplace(H, b) distribution if its PDF is given by: where μ R and b > 0. a) Ifx-Laplace( 0, b-1), find E(X] and Var[X]. b) If X ~ Laplace(p = 0, b 1) and Y bX + μ, show that Y is a Laplace random variable. c) Let Z ~ Laplace(u, b), where μ E R and b > 0. Find E[2] and Var [2]
Show all work! Thank you! kxk-1 4.34 Given the pdf for X is f(x)= 10 0<x<1...
Show all work! Thank you!
kxk-1 4.34 Given the pdf for X is f(x)= 10 0<x<1 otherwise determine E[X] and Var[X]. 1 0<x<1 4.35 Given the pdf for X is f(x)=x. determine E[X] and Var[X]. 10 otherwise' Sections 4.5-4.8 A<x<B 4.36 Given a random variable with pdf f(x)= B-A , determine the MGF for this random variable. 10 otherwise so x50 4.37 Given a random variable with pdf f(x)= betx 0<x , determine the MGF for this random variable. '...
Let X and Y be a random variable with joint PDF: f X Y ( x...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the rand...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y...
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given...
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 <...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x) = to else where c is a positive constant. (a) (5%) Find c. (b) (5%) Find the CDF of X, Fx(x). (c) (5%) Find Prob{2<x<5} (d)(5%) Find E[X], and Var(X).
A continuous random variable Z is said to have a Laplace(H, b) distribution if its PDF is given by: where μ R and b > 0. a) Ifx-Laplace( 0, b-1), find E(X] and Var[X]. b) If X ~ Laplace(p = 0, b 1) and Y bX + μ, show that Y is a Laplace random variable. c) Let Z ~ Laplace(u, b), where μ E R and b > 0. Find E[2] and Var [2]
Show all work! Thank you!
kxk-1 4.34 Given the pdf for X is f(x)= 10 0<x<1 otherwise determine E[X] and Var[X]. 1 0<x<1 4.35 Given the pdf for X is f(x)=x. determine E[X] and Var[X]. 10 otherwise' Sections 4.5-4.8 A<x<B 4.36 Given a random variable with pdf f(x)= B-A , determine the MGF for this random variable. 10 otherwise so x50 4.37 Given a random variable with pdf f(x)= betx 0<x , determine the MGF for this random variable. '...
Let X and Y be a
random variable with joint PDF:
f X Y ( x , y ) = { a
y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise
What is a?
What is the conditional PDF of given ?
What is the conditional expectation of given ?
What is the expected value of ?
Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
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