Let X be the random variable representing the number of calls received in an hou

Question

Let X be the random variable representing the number of calls received in an hour by a 911 emergency service. A probability distribution of X is given below. Value of X 0 1 2 3 4 Probability P(x) 0.3 ____ ____ 0.12 0.06 (a) Suppose the probability that X = 1 and the probability that X = 2 are the same. What are these probabilities? 0.26 Correct: Your answer is correct. (b) What is the probability that at least one call received in an hour? 0.56 Incorrect: Your answer is incorrect. (c) What is the expected number of 911 calls in an hour?

Explanation / Answer

a) Sum of probabilities = 1

Let P(1) = P(2) = y

0.3 + y + y + 0.12 + 0.06 = 1

y = 0.26

b) P(at least 1 call received in a hour) = 1 - P(0)

= 1 - 0.3

= 0.7

c) Expected number of 911 calls received in a hour = 0x0.3 + 1x0.26 + 2x0.26 + 3x0.12 + 4x0.06

= 1.38

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