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- Suppose X and Y are random variables with E[XY ] = 6, E[Y ] = 4 and E[X] = 5 Find Cov(X; Y )Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20, what is P (1 < X < 1.5)?
- Suppose X and Y are the random variables with joint PMF given by: X/Y 11.2 5.75 -3 0 0.07 -2 0.2 0.08 -1 0.1 0.1 0 0.15 0.1 1 0 0.2 a.) Compute E(X2)For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)
- Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.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