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

60. Type i light bulbs function for a random amount of time having mean µ, and standard deviation σι, 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).

61. In Example 4c compute the variance of the length of time until the miner reaches safety.