Use the PMF and CDF from question 5 to answer questions 6, 7, and 8 5. Suppose a

Question

Use the PMF and CDF from question 5 to answer questions 6, 7, and 8 5. Suppose a survey is taken of the number of stoplights in 50 small Texas towns. The results are as follows: 15 towns had zero stoplights, 10 towns had 1 stoplight, 20 towns had 2 stoplights and 5 towns had 3 stoplights. Find the probability mass function (PMF) for X, where X the number of stoplights in the surveyed towns. X 10 15 20 5 (A) 10/50 15/50 2050 5/50 (B) f(r) 15750 25750 45760 1 0 1 2 3 f (r) 15 10 20 5 f(T 15/50 10/50 20/50 550

Explanation / Answer

Let x represent the number of spotlights.

p(x) denotes the probability that number of spotlights is x

n(x) denotes the number of towns with spotlights x

E(x) = Sum( p(x) * n(x) ) = [15/50 * 0 + 10/50*1 + 2*20/50+3*5/50] = 1.3

Hence, expected number of spotlights is 1.3

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