Additional homework 3 problem, not from book. A. Let X be the number of tossess of a fair coin needed to observe two consecutive heads. Determine a closed form expression for the expected value of X. Simplify as much as possible (the final answer has a very simple form). HINT: Recall from last week that the pmf of X is p(x) = FIB(x-1)/(2^x), x=2,3,..., where FIB(k) is the kth term of the Fibonacci sequence. You may assume this formula. Denote a=(1+sqrt(5))/2 and b=(1-sqrt(5))/2. It can be shown that FIB(k) = (a^k - b^k)/sqrt(5). Here, sqrt(5) denotes the positive square root of five. You do not need to prove this result. Optional, no extra credit: To check your result, write a computer program to simulate X. Compute the average of X over a very large number, say 10000, of repititions of this experiment.