5. The number of service calls received by a local fire department is between 0 and 5. The probabilities are 0.10, 0.15, 0.30, 0.20, 0.15, 0.10, respectively. a. Write the probability distribution for the number of service calls in a given day. b. What is the expected number of service calls per day in this fire department

2.45

Step-by-step explanation:

1. Probability distribution shows us sample space(number of calls) and their probabilities

Number of calls. Probability

0. 0.10

1. 0.15

2. 0.30

3. 0.20

4. 0.15

5. 0.19

2. We are to find expected number of calls

(0x0.1) + (1x0.15) + (2x0.30) + (3x0.20) + (4x0.15) + (5x0.10)

E(X) = 0 +0.15 + 0.6 + 0.6 + 0.6 + 0.5

= 2.45

The expected number of Service calls per day is 2.45

Thank you!