The joint PDF of two jointly continuous random variables X and Y is Sc(a? + y²) for 0 < x < 1 and 0 < y< 1, fx,y (x, y) = otherwise. c = 3/2. E(Y) = 5/8. X and are negatively correlated

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: Let X be a uniform random variable over the interval 1 to 4 and Y is exponential with a mean of 2.…

A: Given information: X~Uni(a=1,b=4) Standard deviation of X is: σX=b-a12       =4-112       =0.8660…

Q: (b) Let N(1) be a a zero-mean white Gaussian noise random process. Define V = N(t)dt. Find mean and…

A: Given  N(t) is a zero mean white Gaussian noise random process. To find mean and variance.

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: If X₁, X2, ..., Xn constitute a random sample of size n from an exponential population, show that X…

A: let X1, X2, ......Xn is an independent identically distributed random variable following an…

Q: 2. Let Y₁,..., Yp be independent random variables such that Y~ N(0, 1). Write Y = (Y₁...., Yp) and 0…

A: To show that an unbiased estimator of the risk of the James-Stein estimator iswe can use the…

Q: The joint PDF of two jointly continuous random variables X andY is c(x² + y²) for 0 < x < 1 and 0 <…

A:

Q: Suppose that X and Y are independent random variables with EX=EY=100, and E[min(X,Y)}=79. Find…

A:

Q: The joint PDF of two jointly continuous random variables X and Y is S(x2 +y?) for 0 < x < 1 and 0 <…

A: We have given that,  X and Y two continuous random variables having PDF is,

Q: exponential

A: