The random variable x has the following probability distribution:
x
f(x)
0
.25
1
.20
2
.15
3
.25
4
.15
?
a.Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.b.Calculate the expected value of x.c.Calculate the variance of x.d.Calculate the standard deviation of x.
What will be an ideal response?
| a. | yes f(x)  0 and ? f(x) = 1 |
| b. | 1.85 |
| c. | 2.0275 |
| d. | 1.4239 |
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