-) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0, 1]. The joint pdf of X and Y be given by f(x, y) = 2xy³ - 2y³. Verify if X and Y independent random variables.

Q: Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 0<x<1, 0<y<1-x %3D Find P(Y…

A: Let X and Y continuous random variable with joint pdf fx,y=24xy,   0&lt;x&lt;1, 0&lt;y&lt;1-x…

Q: 3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X²?. Y\X -2 -1 1 2…

A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Random Vector X has the following pdf 1 (2π)n/2.0₁... on Show that the marginal pdf's are Gaussian.…

A: Given:-                         fxX = 12πn/2. σ1.....σn  exp-12∑i=1n xi2σ12

Q: Let Xi and Yi be random variables with Var(Xi) = σx2 and Var(Yi) = σy2 for all i ∈ {1, . . . , n}.…

A: It is given that: varxi=σx2varyi=σy2 and xi and yi are independent and corrxi,yi=ρ

Q: The 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let X and Y be random variables such that var(X) = 16, var (Y) = 9, and p = cor(X, Y) = -0.5. a.…

A: Solution

Q: F(x,y) = { (x+y)/42 ; x = 1,2,3  y = 1,2                 0; elsewhere ] (i) Find the mean for the…

A: F(x,y) : { (x+y)/42 ; x=1,2,3 y=1,2  ; 0 elsewhere } Mean : E(X) = sum(x*P(x))

Q: 3. Suppose X and Y are two independent Gamma random variables: X~ Y Gamma(2, B = 1), where the first…

A:

Q: 0 Find the marginal probability distributions of X and Y. otherwise a) b) Show that the two random…

A:

Q: X is the Gaussian (μ=1, σ=2) random variable. Y is the Gaussian (μ=2, σ=4) radnom variable. X and Y…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let X1,X2,· · ,Xn be i.i.d. random variables, where X; ~ Bernoull Y1 = X1X Y, = X2X %3D Yn-1 = X_ Yn…

A: A random variable X is called to follow the Bernoulli distribution if it takes only non-negative…

Q: Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.

A: Given that X and Y are independent random variables.

Q: ind E (XY ) wvhere X and Y are independent U (0, 1) random variable=

A: