Problem 8A.
Starting at time 0, a red bulb flashes according to a Poisson process with rate λ=2 . Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate λ=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=∞ (i.e., the blue bulb never dies). What is the expected value of the time of the first flash (of either color)?
Expected value of the time of the first flash:
unanswered
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:
unanswered
Problem 8B.
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 e . 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.)
1. Probability that there were exactly 2 arrivals during the time interval [0,2] :
unanswered
Problem 8C.
1. Suppose that X is an exponential random variable with parameter (and mean) equal to 1. Find the MAP estimate of X , given that there were exactly 5 blue flashes.
MAP estimate of X :
1 answer
0 answers