STAT 330

Stat 330 Online: Module 3 Homework Show all of your work, and upload this homework to Canvas. 1. Suppose a continuous random variable X has the following probability density function fX(x) =  cx 0 ≤ x ≤ 2 0 otherwise (a) Find the value of c that makes fX(x) a valid probability density function. (Recall a property that a PDF must have) (b) Give the CDF, FX(x). (c) Find P(0.5 ≤ X ≤ 1.5) using fX(x). (d) Find P(1 ≤ X ≤ 2) using FX(x). (e) Find the value of x such that the pr...

Stat 330: Module 3 Homework Solution Show all of your work, and upload this homework to Canvas. 1. Suppose a continuous random variable X has the following probability density function fX(x) =  kx(1 − x) 0 ≤ x ≤ 1 0 otherwise (a) Find the value of k that makes fX(x) a valid probability density function. (Recall a property that a PDF must have) (b) Give the CDF, FX(x). (c) Find P(0.5 ≤ X ≤ 1) using fX(x). (d) Find P(0 ≤ X ≤ .75) using FX(x). (e) Find E(X). (f) Find V ar...