Exercise 2: Exactly 3 Requests in a Minute, With lambda=5 — Possible Solution
====================================================================

GIVEN
------------------------------
lambda = 5 requests per minute, k = 3

STEP 1: P(EXACTLY 3 REQUESTS)
------------------------------
lambda^k = 5^3 = 125
e^-lambda = e^-5 ~= 0.006738
k! = 3! = 6

P(X=3) = (125 x 0.006738) / 6
        ~= 0.8422 / 6
        ~= 0.1404 (about 14.04%)

STEP 2: E[X] AND Var(X)
------------------------------
Per this chapter's own mean-equals-variance property:

  E[X] = lambda = 5
  Var(X) = lambda = 5

Both the expected number of requests per minute and the variance of
that count are exactly 5 - no separate calculation needed beyond
reading off the rate parameter itself.

WHY THIS WORKS AS AN ANSWER
------------------------------
The exact-count probability is computed using this chapter's own full
Poisson formula with each term shown, while the mean and variance are
read directly from this chapter's own lambda = E[X] = Var(X) property
rather than being computed via a separate, more complex formula.