Consider a random variable XXX whose PDF is f(x)=cx2(1−x)3f(x) = c x^2 (1-x)^3f(x)=cx2(1−x)3 for 0≤x≤10 \leq x \leq 10≤x≤1. What is the variance Var(X)Var(X)Var(X)?
142\frac{1}{42}421
163\frac{1}{63}631
170\frac{1}{70}701
3100\frac{3}{100}1003