Type i light bulbs function for a random amount of time having mean µi and standard deviation σi , i = 1, 2. A light bulb randomly chosen from a bin of bulbs is a type 1 bulb with probability p and...

Type i light bulbs function for a random amount of time having mean µi and
standard deviation σi
, i = 1, 2. A light bulb randomly chosen from a bin of bulbs is a
type 1 bulb with probability p and type 2 bulb with probability 1 −p. Let X denote the
lifetime of this bulb. Find:
(a)  E(X);
(b)  Var(X)