The part within braces are only for better understanding.

3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W...
. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X = ZY. (a) Compute E(XY). (b) Compute E(X).
4. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X Z (a) Compute E(XTY). (b) Compute E(X).
Let X and Y be independent uniform distributed random variables, 0 < X < 1 and 1 < Y < 2. Let Z = X + Y. What is the pdf of Z?
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x > 0) and f(y) = µe-µy (y > 0) respectively. (i) Let Z = min(X, Y ). Find f(z), E(Z), and Var(Z). (ii) Let W = max(X, Y ). Find f(w) (it is not an exponential pdf). (iii) Find E(W) (there are two methods - one does not require further integration). (iv) Find Cov(Z,W). (v) Find Var(W).
Let X 1 and X 2 be statistically independent and identically distributed uniform random variables on the interval [ 0 , 1 ) F X i ( x ) = { 0 x < 0 x 0 ≤ x < 1 1 x ≥ 1 Let Y = max ( X 1 , X 2 ) and Z = min ( X 1 , X 2 ) . Determine P(Y<=0.25), P(Z<=0.25), P(Y<=0.75), and P(Z<=0.75) Determine
Problem 5 Suppose X and Y are independent random variables following Uniform[0, 1]. Let Z- (X +Y)/2. (1) Calculate the cumulative density of z. (2) Calculate the density of Z. Problem 5 Suppose X and Y are independent random variables following Uniform[0, 1]. Let Z- (X +Y)/2. (1) Calculate the cumulative density of z. (2) Calculate the density of Z.
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0, 1]. Let Y1 = min(X1, ,X, and Yn = mar(X1,-..,X,H a. Show that Fri (y) = P(Ks y)-1-(1-Fri (y))". b. Show that and Fh(y) = P(, y) = (1-Fy(y))". c. Using the results from (a) and (b) and the fact that Fy (y)-y by property of uniform distribution on [0, 11, find EMI and EIYn]
Let X and Y be independent random variables with pdf 2-y , 0sys2 2 f(x) 0, otherwise 0, otherwise ) Find E(XY) b) Find Var (2X+3Y)
The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random variables Z and W (b) Find the density of random variable W (c) Find the density of random variable Z The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random...