Let N be the number of requests to a web server per day and let N...

Let N be the number of requests to a web server per day and let N Poisson(). Each request

comes from a human with probability p or from a spam bot with probability 1 ? p. Assume that

the requests are independent of each other. Let X be the number of requests from humans per

day and Y be the number of requests from spam bots per day.

(a) State the conditional distribution of X given N = n, and state the conditional distribution of

Y given N = n.

(b) Calculate the probability of getting exactly x human requests and y spam requests.

(c) Find the joint probability mass function of X and Y , and show that X and Y are independent

of each other.

(d) Using your result in part (c), compute E[X + Y ] and Var[X + Y ].

Expert Solution

orchestra answered 2 years ago

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