Suppose that X has the probability density function f(x) = { 2x 0 < x < 1 0 otherwise Which of the following is the moment generating function of X? 2 et t 2 et t2 2 t2 O t2 2 eet t 2 ett t2 t e eut-1 t
Problem 2 (20 points) Suppose (Y,X) e R × 10, îl has joint density 1/2e-0.5(y+) T (a) Find the marginal density of Y (b) Find the marginal density of X (c) Deduce P10.7 < X 〈 0.81. (d) Are Y and X independent? Problem 2 (20 points) Suppose (Y,X) e R × 10, îl has joint density 1/2e-0.5(y+) T (a) Find the marginal density of Y (b) Find the marginal density of X (c) Deduce P10.7
Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0. Let Y = √X. a. Find the cdf for Y. b. Find the pdf for Y. c. Find E[Y]. If you want to skip a difficult integration by parts, make a substitution and look for a Gamma pdf. d. This Y is actually a commonly used continuous distribution. Can you name it and identify its parameters? e. Suppose that X is exponentially distributed with...
Find f(x) if fx)= sec x-2e and f(0) 0 2 Find f(x) if fx)= sec x-2e and f(0) 0 2
Suppose that the density function of a continuous random variable is given by f(x)=c(e-2x-e-3x) for non-negative x, and 0 elsewhere a) Determine c b) Compute P(X>1) c) Calculate PX<0.5 X<1.0)
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1
- 2x Find the values of x at which the function f(x)=e + 2x has a relative maximum or minimum point. O A. minimum at x = 0 OB 0.69 maximum at x = 2 O C. There are no relative maximum/minimum points. OD maximum at x- O E. none of these Click to select your answer
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
Problem 2 If Xi, X2. ,Xso be independent and idatically distributed with probability density function same as random variable X (x) = 1/2e-2x x > 0 and Y-X1 X2+X Points 5 Points) 5 Points a) Find Moment Generating Function of Y, My(S) b) What is MGF of-2x c What is MGF of 2X +3 Problem 2 If Xi, X2. ,Xso be independent and idatically distributed with probability density function same as random variable X (x) = 1/2e-2x x > 0...
Given that the random variable X has density function 7. 2x, 0<x <a f(a)-t o, otherwise a) Determine a. Find. P (2 < X < 4) and P (-2 < X < 2 b) Determine the parameter A in PDF given by the formula: f(x) -AeAt. Calculate the probabilities given in the above intervals of x Given that the random variable X has density function 7. 2x, 0