Discrete Random Variables

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1. The volunteer fire department handles between 0 to 5 calls on any given day. The probability distribution for the number of service calls is [15 points]

 

Number of calls                Probability

0                                  .20

1                                  .30

2                                  .20

3                                  .10

4                                  .10

5                                  .10

 

 

1. Is this a valid probably assignment? Explain.(3 points)

 

 

 

 

 

1. What is the random variable in this problem?(2 points)

 

 

 

 

 

 

1. What is the probability that the fire department handles at least 3 service calls on a given day?(2 points)

 

 

 

 

 

 

1. What is the probability that the fire department handles at most 2 service calls on a given day?(2 points)

 

 

 

 

 

 

 

1. What is the expected number of service calls?(2 points)

 

 

 

 

 

 

 

 

 

 

1. What is the variance in the number of service calls?(2 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. What is the standard deviation?(2 points)

 

 

 

2. Seven plants are operated by a garment manufacturer. They feel there is a ten percent chance for a strike at any one plant and the risk of a strike at one plant is independent of the risk of a strike at another plant.[25 points]

 

1. What is the random variable in this problem? (2 points)

 

 

 

1. What is (4 points)
2. What is defined as a “success”?

 

 

 

 

2. What is the probability of success?

 

 

 

3. What is defined as a “failure”?

 

 

 

 

4. Calculate the probability of failure.

 

 

 

 

1. Write the probability density function.(3 points)

 

 

 

 

1. What is the probability at most three plants will strike? (2 points)

 

 

 

 

 

 

1. What is the probability that none of the plants will strike? (2 points)

 

 

 

 

 

1. What is the probability that two of the plants will strike? (2 points)

 

 

 

 

 

1. What is the probability that at least one of the plants will strike? (2 points)

 

 

 

 

 

 

1. What is the probability that between four and six (inclusive) of the plants will strike? (2 points)

 

 

 

 

 

1. What is the expected number of plants that will strike? (2 points)

 

 

 

 

 

 

1. What is the variance in the number of plants that will strike? (2 points)

 

 

 

 

 

 

1. What is the standard deviationof the number of plants that will strike? (2 points)