Random variables X & Y are distributed according to ( f,y ) = x+y , 0 < x < 1, 0 < y< 1
Calculate P(X > √ Y)
Random variables X & Y are distributed according to ( f,y ) = x+y , 0 < x < 1, 0 < y...
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
3. The random variables X and Y are independent and identically distributed (iid) according to the uniformd
Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y < 0 for 0 <x< 1 and 0 <y<1 1. for x > 1 and y> 1 a) Find the joint and marginal pdfs. b) Use F(x, y) and find P(X<0.75, Y> 0.25), P(X<0.75, Y = 0.25), P(X<0.25)
Let X, Y , Z be uniformly distributed random variables on the interval [0, 2]. Calculate the probability that they are ordered as X < Y < Z. That is, calculuate P(X < Y < Z).
9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Y|Y -1 0 1 0.1 0.1 0.1 3 0 0.2 0.1 4. 0.2 0.1 0.1 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
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, Y be random variables with f(x, y) = 1,-y < x < y, 0 < y < 1. Show that Cov(X,Y) = 0. Are X, Y independent?
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
The joint density of random variables X and Y is given to be f(x,y) =xy^2 for 0≤x≤y≤1 and is 0 elsewhere. (a) Compute the marginal densities for X and for Y respectively. (b) Compute the expected valueE(XY). (c) Define a new random variable W=Y/X. Compute the probability P(W > t) for anyt >1. Also find the probability P(W <1/2) ?
f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability density function 12, 0<x<1, 0<y<0.5 else a) (5 marks) Find P(X - Y <0.25). b) (5 marks) Find P(XY <0.30). c) (5 marks) Find V (2x - 5Y+30).