Suppose we have a discrete r.v $X$ where $P(X=0) = 0.3$ and $P(X=U)=0.7)$ where U ~ Uniform(1,51).
How do we calculate E(X) and Var(X)?
Intuitively I understand E(X) should be $0*0.2+E(U)*0.8$ but I'm struggling to see why this is true mathematically. I'm lost on the variance. Thanks!