7. Let X be a random variable with density f(x) = 2/32 for 1<x<2, f(x) =...
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
4. [10 pts] Let X be a random variable with probability density function if 1 < a < 2, 2 f(a)a 0 otherwise. Find E(log X). Note: Throughout this course, log = loge.
Suppose the density for a random variable is given by the following: f(x) = Cz" for 1 < x < 2, and f(x) = 0 otherwise. Find the value of C, and then find the mean of this random variable.
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
Let X be a random variable with a density function given by 2 NI W x – 1 < x < 1 f(x) = 6e elsewhere a) Find the density function of Y = 3 – X. b) Find the density function of Y = X2.
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
8. Suppose X is a continuous random variable with density f(x) = 1/3,-1 < x < 0, f(x) = 2(z-1)2,1 < x < 2, and 0 everywhere else. (a) Find E(X).