Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a}) (i) (ii) Show that X and Y are zero mean random variables. Are X and Y correlated?
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- A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
- Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over the square whose vertices are (1, 0), (0, 1), (−1, 0), and (0, −1). Find the Correlation Coefficient ρxyLet X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]