Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf

f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0

0 otherwise

Find Cov(X2, X3)

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the...

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1...

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1 X2 = 2θ + ε2 X3 = 3θ + ε3 ε1, ε2, ε3 are independent and the mean and variance are the following random variable E(ε1) = E(ε2) = E(ε3) = 0 Var(ε1) = 4 Var(ε2) = 6 Var(ε3) = 8 What is the Best Linear Unbiased Estimator(BLUE) when estimating parameter θ from the three samples X1, X2, X3

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2...

Let X1,X2,X3 be i.i.d. N(0,1) random variables. Suppose Y1 = X1 + X2 + X3, Y2 = X1 −X2, Y3 =X1 −X3. Find the joint pdf of Y = (Y1,Y2,Y3)′ using : Multivariate normal distribution properties.

Let X and Y be two jointly continuous random variables with joint PDF f(x,y) = Mxy^2...

Let X and Y be two jointly continuous random variables with joint PDF f(x,y) = Mxy^2 0<x<y<1 a) Find M = ? b) Find the marginal probability densities. c) P( y> 1/2 | x = .25) = ? d) Corr (x,y) = ?

Let X1, X2, X3, . . . be independently random variables such that Xn ∼ Bin(n,...

Let X1, X2, X3, . . . be independently random variables such that Xn ∼ Bin(n, 0.5) for n ≥ 1. Let N ∼ Geo(0.5) and assume it is independent of X1, X2, . . .. Further define T = XN . (a) Find E(T) and argue that T is short proper. (b) Find the pgf of T. (c) Use the pgf of T in (b) to find P(T = n) for n ≥ 0. (d) Use the pgf of...

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1 0 < x2 < 1 , otherwise (ii) Calculate E(X1) and E(X2) (iii) Are the variables X1 and X2 stochastically independent? (iv) Given the variables in the question, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1...

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1 > 0, x2 > 0 0 elsewhere . For constants w1 > 0 and w2 > 0, let W = w1X1 + w2X2. (a) Show that the pdf of W is fW (w) = " 1 w1− w2 (e−w/w1 − e−w/w2) w > 0 0 elsewhere . (b) Verify that fW (w) > 0 for w > 0. (c) Note that the pdf fW...

Let X1,…, Xn be a sample of iid random variables with pdf f (x; ?1, ?2)...

Let X1,…, Xn be a sample of iid random variables with pdf f (x; ?1, ?2) = ?1 e^(−?1(x−?2)) with S = [?2, ∞) and Θ = ℝ+ × ℝ. Determine a) L(?1, ?2). b) the MLE of ?⃗ = (?1, ?2). c) E(? ̂ 2).

Consider independent random variables X1, X2, and X3 such that X1 is a random variable having...

Consider independent random variables X1, X2, and X3 such that X1 is a random variable having mean 1 and variance 1, X2 is a random variable having mean 2 and variance 4, and X3 is a random variable having mean 3 and variance 9. (a) Give the value of the variance of X1 + (1/2)X2 + (1/3)X3 (b) Give the value of the correlation of Y = X1- X2 and Z = X2 + X3.

Subjects