2. (5 marks) Consider a random variable Y with density function 31 ,else Find the probability...
Use the method of distribution functions 2. (5 marks) Consider a random variable Y with density function 3y2 0 ,else Find the probability density function of U 4-Y
Use the Method of Distribution Functions 2. (5 marks) Consider a random variable Y with density function 3 v 0 .else Find the probability density function of U 4- r2
3. (5 marks) The joint density of X and Y is given as else Find the probability density function of U-X-Y.
If X ~U(-2; 4), find the probability density function of the random variable: a) Y = 2X + 3. b) Y = 1/(X+2)4 c) Y = X2u(X), where u(x) is the unit step function. Hint: first sketch g(x) = x2u(x)
6. (5 marks) The joint density of X and Y is given as 0, else Find the probability density function of U-Y/X. Use any method you wish.
6. (5 marks) The joint density of X and Y is given as 0, else Find the probability density function of U-Y/X. Use any method you wish
1. (15 marks) The joint density of X and Y is given as f(x.))-o, else a) (5 marks) Find the probability density function of W-Y", where a>0 b) (5 marks) Find the probability density function of U- XY 0(5 marks) Find the probability density function of V-X-Y
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
9. (5 marks) Consider a Gamma random variable, Y ~ Ganzma(α = n/2, β). Find the moment- generating function of U = c Y. If U ~ , what is c?