On a multiple choice question with 6 choices, a certain student either knows the answer and then marks the correct choice or doesn't know the answer and then marks one of the choices at random. What is the probability that she knew the answer if she marked the correct choice? Assume the prior probability that she knew the answer is 2/3.
Let X be a random variable with probability distribution function
fx(x) = { Ax^2, if x is an element of [-2,2]
{ 0, if x is not an element of [-2,2]
Find the constant A and the cumulative distribution function Fx. Also find E(X), Var(X)