this is tricky, have to solve it. come on everyone lets think and try fr possible sol

1. An experiment is conducted repeatedly. At each trial the outcome is either failure or success. The outcome of each trial is independent of all others. It is known that where . a) Define the random variable to equal the number of trials necessary to have the first success, and the event . Determine the values that the conditional random variable takes on and the corresponding probabilities, the conditional mean, namely , and the conditional variance. b) Define the random variable to equal the number of trials necessary to have three successes for the first time, and the event . Determine the values that the conditional random variable takes on and the corresponding probabilities, the conditional mean and the conditional variance. c) Evaluate the conditional means and conditional variances of parts a) and b) for . Hint: a check on the validity of the results in parts a) and b) is possible by showing that the PMF of each conditional random variable sums to 1.

Re: this is tricky, have to solve it. come on everyone lets think and try fr possible

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