Question: Type i light bulbs function for a random amount of time having mean i and standard deviation i, i = 1, 2. A light bulb

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 a type 2 bulb with probability 1 − p. Let X denote the lifetime of this bulb. Find
(a) E[X];
(b) Var(X).

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