. Suppose N has a binomial distribution with n = 10 and p = 0.3. (a) Using the formula (2.17), calculate P(N = 0), P(N = 2), E(N), and VarN. (b) Using R and Computational Example 2.2, simulate...

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Suppose N has a binomial distribution with n = 10 and p = 0.3.

(a) Using the formula (2.17), calculate P(N = 0), P(N = 2), E(N), and VarN.

(b) Using R and Computational Example 2.2, simulate observations from N.

Use the simulated values to estimate the probabilities you calculated in

(a), and compare with the results in (a).

(c) Now use R to simulate observations from N when n = 1000 and p = 0.25.

What is your estimate of P(N ≥ 280)? (See (2.20).)