Question: 1. Let T ~ gamma (20, 0.0002) be the total operating time for the units described in Exercise.

a. Use the m-function for the gamma distribution to determine P (T ≤ 100; 000).

b. Use the Poisson distribution to determine P (T ≤100; 000).

Exercise: Twenty "identical" units are put into operation. They fail independently. The times to failure (in hours) form an iid class, exponential (0.0002). This means the "expected" life is 5000 hours. Determine the probabilities that at least k, for k = 5; 8; 10; 12; 15, will survive for 5000 hours.

2. The sum of the times to failure for five independent units is a random variable X~ gamma (5; 0:15). Without using tables or m-programs, determine P (X ≤ 25).