Problem to think about will not be graded, but strongly encouraged to think abou

Question

Problem to think about will not be graded, but strongly encouraged to think about!) Consider Problem #1 with the following change: When the frog jumps and fails to reach the next step, it rolls back down to the bottom and has to start all over again. Let Y be the number of jumps it takes for the frog to escape the well. What is EY]? A frog is trapped in a well. In order to escape from the well the frog needs to climb up three steps. The frog can jump high enough for one step at a time However, it needs to jump at a certain angle in order to land on the next step successfully. Each time it jumps it successfully jumps to the next step with probabty . Otherwise, it hits the vertical side of the stair and bounces back to where it was ty 1-q and tries again starting from the same step. Let X denote the number of jumps the frog makes before it escapes the well

Explanation / Answer

Negative binomial distribution is suitable. We dont know number of failures but only number of success required. also probability of both are known and so negative binomial distribution gives the expected result.

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