Type i light bulbs function for a random amount of time having mean μ_{i} and standard deviation σ_{i},i=1,2. A light bulb randomly chosen from a bin of bulbs is a type 1 bulb with probability p and a type 2 bulb with probability 1-p. Let X denote the lifetime of this bulb.

Find

(a) E[X];

(b) Var(X).