# Question: Generalize Exercise 5 4 3 by showing that the sum of n

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1, μ2, . . . , μn is Poisson with mean

μ1 + μ2 + · · · + μn.

μ1 + μ2 + · · · + μn.

## Answer to relevant Questions

Let X1, X2, X3, X4, X5 be a random sample of size 5 from a geometric distribution with p = 1/3. (a) Find the mgf of Y = X1 + X2 + X3 + X4 + X5. (b) How is Y distributed? Let n = 9 in the T statistic defined in Equation 5.5-2. (a) Find t0.025 so that P(−t0.025 ≤ T ≤ t0.025) = 0.95. (b) Solve the inequality [−t0.025 ≤ T ≤ t0.025] so that μ is in the middle. Suppose that the sick leave taken by the typical worker per year has μ = 10, σ = 2, measured in days. A firm has n = 20 employees. Assuming independence, how many sick days should the firm budget if the financial officer ...Let Y equal the sum of n = 100 Bernoulli trials. That is, Y is b(100, p). For each of (i) p = 0.1, (ii) p = 0.5, and (iii) p = 0.8, (a) Draw the approximating normal pdfs, all on the same graph. (b) Find P(| Y/100 − p | ...The probability that a certain type of inoculation takes effect is 0.995. Use the Poisson distribution to approximate the probability that at most 2 out of 400 people given the inoculation find that it has not taken effect.Post your question