In a super fast photonic switch that you are designing, each incoming photon is directed to...

In a super fast photonic switch that you are designing, each incoming photon is directed to output port ”A” with probability p, and to output port B with probability 1 − p, independently. Let R be the total number of photons going to port A and let G be the number of items going to port B in a certain amount of time, during which n photons pass through the switch.

(a) Determine the PMF, expected value, and variance of the random variable R.

(b) Evaluate P(A), the probability that the first photon ends up being the only one sent to its port.

(c) Find P(B), the probability that at least one port ends up receiving exactly one photon in this time interval.

(d) Evaluate the expectation and variance for the difference, D = R − G.

(e) Assume n ≥ 2. Given that both of the first two input photons go to port A, find the conditional expectation, variance and PMF of R.

Expert Solution

orchestra answered 1 year ago

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In a super fast photonic switch that you are designing, each incoming photon is directed to...

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