# Question: Type i light bulbs function for a random amount of

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).

(a) E[X];

(b) Var(X).

## Relevant Questions

The number of winter storms in a good year is a Poisson random variable with mean 3, whereas the number in a bad year is a Poisson random variable with mean 5. If next year will be a good year with probability .4 or a bad ...Suppose that A and B each randomly and independently choose 3 of 10 objects. Find the expected number of objects (a) Chosen by both A and B; (b) Not chosen by either A or B; (c) Chosen by exactly one of A and B. N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or she has any friends among those present. That person then sits either at the table of a friend or at an unoccupied table if ...In Example 4f, we showed that the covariance of the multinomial random variables Ni and Nj is equal to −mPiPj by expressing Ni and Nj as the sum of indicator variables. We could also have obtained that result by using the ...Prove Proposition 2.1 when (a) X and Y have a joint probability mass function; (b) X and Y have a joint probability density function and g(x, y) ≥ 0 for all x, y.Post your question