Consider the random variable X whose probability density function is given by k/x3 if x>r fx(x)...
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
The random Variable X has a pdf fx (2) = {*** kr + > -1 <r<2 otherwise Y is a function of X and is derived using Y = g(x) = X S -X X2 X <0 X>0 Find: (A) fr(y) (B) E[Y] using fy(y) (C) EY] using fx (2)
10. Let X be a continuous random variable with probability density function -T xe h(x) = { x > 0 x < 0 0 a. Verify that h(x) is a valid probability density function. [7] b. Compute the expected value E(X) and variance V(X) of X. [8]
10. Let X be a continuous random variable with probability density function -2 хе x > 0 h(z) = { { 0 x < 0 a. Verify that h(x) is a valid probability density function. [7] b. Compute the expected value E(X) and variance V(X) of X. [8]
2. A random variable has a probability density function given by: Bmx-(B+1) x20 x<m fx(x)= 10 where m>0 and B > 2. Let m and ß be constants; answer the questions in terms of m and B. (a) Find the cumulative distribution function (cdf) Fx(x) of this random variable; (b) Find the mean of X; (c) Find E[X']; and (d) Find the variance of X. [12 points]
If the probability density function of X is given by n2 for 1<x< 2 fx ) = 10 elsewhere (a) Find, E[X], E[X2], and E[X3] (b) Use your answer to part (a) to find E[X3 + 3X2 - 2x + 5)
The random variable X has the following probability density function: fx(x) = kxo e-0.02x , x > 0, k is a constant. Calculate ELX] A50 B3oo C 2,500 10,000 E140,000
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].