Please answer the third (8c) question (last question) while ignoring the answers provided. Thank you.

Problem 8(b) 2 points possible (graded, results hidden] Suppose that X is equal to either 1 or 2, with equal probability. Write down an expression for the probability that there were exactly 2 arrivals during the time interval [0, 2]. (Enter e for the constant 6. You may use standard notation for this numerical entry even though there will be no parser below the answer box. Enter an exact answer or a numerical answer accurate to at least 3 decimal places.) Probability that there were exactly 2 arrivals during the time interval [0, 2]: 0.06442 Suppose that X is an exponential random variable with parameter (and mean} equal to 'I. Find the MAP estimate of X, given that there were exactly 5 blue flashes. MAP estimate of X: 5f3 Starting at time 0, a red bulb flashes according to a Poisson process with rate A = 2. Similarly, starting at time 0; a blue bulb flashes according to a Poisson process with rate A = 1, but only until a nonnegative random time X, at which point the blue bulb "dies." We assume that the two Poisson processes and the random variable X are [mutually] independent. 1. Suppose that X is deterministically equal to 1. What is the expected total number of flashes (of either color] during the interval [0, 2]? EXDECtEd tetal number Of asrles; 2. In the time interval [0, X], there are exactly 5 flashes. What is the probability that exactly 2 of them were red? Probability that exactly 2 of the 5 flashes were red: 0.0512