Similar to Homework 5, we encounter a sequence of boobies while walking in the Galapagos. Boobies can either be blue-footed (B) or red-footed (R). We let X be the random variable corresponding to the number of boobies we encounter until seeing the first blue one. (That is, if we see the pattern RRRB, X = 4.) Suppose each boobie is red-footed with probability I- ? and blue-footed with probability p. Determine the conditional PMF ?x| x le N(k) as a function of ? and N. Compute E(X | X le 5) when ? = 1/4. Use a property from class to determine E(X | X > 5) when ? = 1/4. Hint: you don\'t have to do any complicated computation here if you understand what type of random variable this is. Solution a) P(X=k) / P(X5) = 1- P(X<=5) using that The Expectation can be easily computed ...