# Expected value of random variable

Given the following probability distributions:

Distribution A Distribution B

X P(X) X P(X)

0 0.50 0 0.05

1 0.20 1 0.10

2 0.15 2 0.15

3 0.10 3 0.20

4 0.05 4 0.50

a. Compute the expected value for each distribution.

b. Compute the standard deviation for each distribution.

c. Compare and contrast the results of distributions A and B.

The following table contains the probability distribution for the number of traffic accidents daily in a small city.

Number of Accidents Daily (X) P(X)

0 0.10

1 0.20

2 0.45

3 0.15

4 0.05

5 0.05

a. Compute the mean or expected number of accidents per day.

b. Compute the standard deviation.

See attached file for full problem description.

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#### Solution Preview

Please see attached file.

Compute the expected value for each distribution.

Distribution A ...

#### Solution Summary

Calculation of expected value, standard deviation and variance of a random variable.