2)
The cummulative distibution function od U is given by:
Now,
which is the PDF of U.
Use the Method of Distribution Functions 2. (5 marks) Consider a random variable Y with density...
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 3. (5 marks) The joint density of X and Y is given as , else Use the Method of Distribution Functions Find the probability density function of U- X-Y.
Use the method of distribution functions 3. (5 marks) The joint density ofX and Y is given as 0 , else Find the probability density function of UX-Y.
2. (5 marks) Consider a random variable Y with density function 31 ,else Find the probability density function of U 4-Y2
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...
I. Let the random variable y have an uniform distribution with minimum value θ = 0 and maximum value θ2-1 and let the random variable U have the form aY +b, where a and b are both constants and a > 0. (a) Using the transformation method, find the probability density function for the random variable U when a 2 and b-4. What distribution does the random variable U have? (b) Using the transformation method, find the probability density function...
Consider the random variable Y, whose probability density function is defined as: if 0 y1 2 y if 1 y < 2 fr(v) 0 otherwise (a) Determine the moment generating function of Y (b) Suppose the random variables X each have a continuous uniform distribution on [0,1 for i 1,2. Show that the random variable Z X1X2 has the same distribution = as the random variable Y defined above. Consider the random variable Y, whose probability density function is defined...
5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter β. Let ?? = √??. Find the pdf of U. Note: U has a Weibull distribution. You will see the Weibull distribution many times in this course 5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter B. Let U-VY. Find the pdf of U. Note: Uhas a...
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