Question

A continuous variable X takes values from 0 to 2. the probability that X takes a value greater than x is px^2 + q for 0≤ x ≤2. Determine the value for p and q. Find the probability density function.

Answer 1

F(x)=P(X<x)=1-px^2-q

So F is the CDF of X and so we know that F(0)=0 and F(2)=1, use that to find p and q.