# Question: In Example 5c compute the variance of the length of

In Example 5c, compute the variance of the length of time until the miner reaches safety.

Example 5c

A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him to safety after 3 hours of travel. The second door leads to a tunnel that will return him to the mine after 5 hours of travel. The third door leads to a tunnel that will return him to the mine after 7 hours. If we assume that the miner is at all times equally likely to choose any one of the doors, what is the expected length of time until he reaches safety?

Example 5c

A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him to safety after 3 hours of travel. The second door leads to a tunnel that will return him to the mine after 5 hours of travel. The third door leads to a tunnel that will return him to the mine after 7 hours. If we assume that the miner is at all times equally likely to choose any one of the doors, what is the expected length of time until he reaches safety?

## Answer to relevant Questions

Consider a gambler who, at each gamble, either wins or loses her bet with respective probabilities p and 1 − p. A popular gambling system known as the Kelley strategy is to always bet the fraction 2p − 1 of your current ...Suppose that in Problem 70 we continue to flip the coin until a head appears. Let N denote the number of flips needed. Find (a) P{N ≥ i}, i ≥ 0; (b) P{N = i}; (c) E[N]. Problem 70 Consider an urn containing a large ...Show that E[(X − a)2] is minimized at a = E[X]. Suppose that X is a continuous random variable with density function f. Show that E[|X − a|] is minimized when a is equal to the median of F. Write Now break up the integral into the regions where x < a and where x > a, ...An urn initially contains b black and w white balls. At each stage, we add r black balls and then withdraw, at random, r balls from the b + w + r balls in the urn. Show that E[number of white balls after stage t] = (b + w / ...Post your question