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Problem Biol 2 points possible [grade-cl. results hidden]: Starting at time D, a red bulb flashes according to a Poisson process with rate A = 2. Similarly, starting at time El, a blue bulb {lashes according to a Poisson process with rate Jr 2 1, but only until a nonnegatilre 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 hteryai [I]. 2]? Expected total number of flash es: 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 ashes were red: Problem 8{b) 2.0 points possible tgraded, results hidden] Eupoose that X is equal to either i or 2. with equal probability. illirite down an expression for the probability that there were exactly 2 arrivals sharing;l the time interval [0,2]. {Enter a for the constant '5. You may Its-E standard notation for this numerical with; even though there Will be I10 parser below the answer bolt. 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]: Scroll Down: There is one more problem below. Subm'i You have used a of 3 attempts Problem S{c) 2.0 points possible (graded. results hiddeni Suppose that X is an exponential random variable with parameter iano mean] equal to 1. Find the MAP estimate of X, given that there were exactly 5 blue esne 3. MAP estimate of