Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Question

Question

Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2.
(a) Find the CDF and PDF of Y =X1 + 2X2 .
(b) Find the CDF of Z = Y + X3 .
(c) Find the joint PDF of Y and Z . (Hint: Try the trick in Problem 2(b))

engineering Electrical-Engineering

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Given v나 (O 4 -2 de卜〉S 4 -4 Ys 2. cof

Add a comment

Answer 2

Similar Homework Help Questions

Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the tri...

Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the trick in Problem 2(b) Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c)...
Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate...

Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate 1. Let: Y = X1 + X2 , Z = X1 − X2 (a) What is the cdf of X1? (b) What is the joint pdf of (X1, X2)? (c) What is the joint pdf of (Y, Z)? (d) What is the marginal pdf of Z?
Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let...

Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let Y- max(Xi, X2, X3). Find the cdf of Y (c) Derive the pdf of Y

2. Let Xi exp(1) and X2 ~ variables with rate 1. Let: erp(1) be independent and...

2. Let Xi exp(1) and X2 ~ variables with rate 1. Let: erp(1) be independent and identically-distributed exponential random (a) What is the cdf of X1? b) What is the joint pdf of (Xi, X2)? (c) What is the joint pdf of (Y, Z)? d) What is the marginal pdf of z?
Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and...

Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and E(X3) = 3. Let Y = 3X1 − 2X2 + X3. Find E(Y ), Var(Y ) in the following examples. X1, X2, X3 are Poisson. [Recall that the variance of Poisson(λ) is λ.] X1, X2, X3 are normal, with respective variances σ12 = 1, σ2 = 3, σ32 = 5. Find P(0 ≤ Y ≤ 5). [Recall that any linear combination of independent normal...
Let (X1,X2,X3) have the joint pdf fx(x1, x2, x3) = k*x1*x2*x3; 0 < x1 < x2...

Let (X1,X2,X3) have the joint pdf fx(x1, x2, x3) = k*x1*x2*x3; 0 < x1 < x2 < x3 < 1. Consider the transformation U1 = X1/X2; U2 = X2/X3; U3 = X3. a) Find the value of k. b) Find the joint pdf fu(u1, u2, u3) of U1,U2,U3.

= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) =...

= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the...

Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the unit interval, (0,1) Introduce two new random variables, M-max (X1, X2,..., Xn) and N -min (X1, X2,..., Xn) 1. Find the joint distribution of a pair (M,N) 2. Derive the CDF and density for M 3. Derive the CDF and density for N.
Let X1,X2 be two independent exponential random variables with λ=1, compute the P(X1+X2<t) using the joint...

Let X1,X2 be two independent exponential random variables with λ=1, compute the P(X1+X2<t) using the joint density function. And let Z be gamma random variable with parameters (2,1). Compute the probability that P(Z < t). And what you can find by comparing P(X1+X2<t) and P(Z < t)? And compare P(X1+X2+X3<t) Xi iid (independent and identically distributed) ~Exp(1) and P(Z < t) Z~Gamma(3,1) (You don’t have to compute) (Hint: You can use the fact that Γ(2)=1, Γ(3)=2) Problem 2[10 points] Let...

(a) Consider four independent rolls of a 6-sided die. Let X be the number of l's...

(a) Consider four independent rolls of a 6-sided die. Let X be the number of l's and let y be the number of 2's obtained. What is the joint PMF of X and Y? (b) Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is the middle of the three values). Find the conditional CDF of X1, given that Y = 0.5. Under this conditional distribution, is...

Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Homework Answers

Add Answer to:
Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Post as a guest

Earn Coins

Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the tri...

Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate...

Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let...

2. Let Xi exp(1) and X2 ~ variables with rate 1. Let: erp(1) be independent and...

Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and...

Let (X1,X2,X3) have the joint pdf fx(x1, x2, x3) = kx1x2*x3; 0 < x1 < x2...

= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) =...

Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the...

Let X1,X2 be two independent exponential random variables with λ=1, compute the P(X1+X2<t) using the joint...

(a) Consider four independent rolls of a 6-sided die. Let X be the number of l's...

Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Homework Answers

Add Answer to: Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....

Post as a guest

Earn Coins

Add Answer to:
Let X1 , X2 , and X3 be independent and uniformly distributed between -2 and 2....