Suppose X has probability density function f(x)=6x(1-x) for 0<x<1 and 0 otherwise. What is E[X] and Var[X]? Statistics Random Variables Probability Distribution 1 Answer De Rono Oct 27, 2015 #E[X]=1/2# and #Var[X}= 1/20# Explanation: #E[X] = int_0^1 6x^2(1-x)dx= 1/2# and #E[X^2] = int_0^1 6x^3(1-x)dx= 3/(10)# So #Var[X]= E[X^2]-(E(X))^2=3/(10)- 1/4=1/20# Answer link Related questions What is the difference between a discrete random variable and a continuous random variable? What is the sum of the probabilities in a probability distribution? What is an example of a continuous random variable? How are random variables generally identified (i.e., what notation is used to identify a random... What does the term "expected value" mean? What notation is used to designate the expected value of a random variable? You roll three dice, and you define the random variable #X# as the number of heads obtained. ... You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm... You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm... You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm... See all questions in Probability Distribution Impact of this question 35467 views around the world You can reuse this answer Creative Commons License