Type i light bulbs function for a random amount of time having mean  and standard deviatio...

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

(a) E[X];

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(b) Var(X).