# 4.S: Random Variables (Solutions- Practice + Homework)

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1.

$$x$$ $$P(x)$$
0 0.12
1 0.18
2 0.30
3 0.15
4 0.10
5 0.10
6 0.05
Table $$\PageIndex{6}$$

3.

0.10 + 0.05 = 0.15

5.

1

7.

0.35 + 0.40 + 0.10 = 0.85

9.

1(0.15) + 2(0.35) + 3(0.40) + 4(0.10) = 0.15 + 0.70 + 1.20 + 0.40 = 2.45

11.

$$x$$ $$P(x)$$
0 0.03
1 0.04
2 0.08
3 0.85
Table $$\PageIndex{7}$$

13.

Let $$X =$$ the number of events Javier volunteers for each month.

15.

$$x$$ $$P(x)$$
0 0.05
1 0.05
2 0.10
3 0.20
4 0.25
5 0.35
Table $$\PageIndex{8}$$

17.

1 – 0.05 = 0.95

18.

$$X =$$ the number of business majors in the sample.

19.

2, 3, 4, 5, 6, 7, 8, 9

20.

$$X =$$ the number that reply “yes”

22.

0, 1, 2, 3, 4, 5, 6, 7, 8

24.

5.7

26.

0.4151

28.

$$X =$$ the number of freshmen selected from the study until one replied "yes" that same-sex couples should have the right to legal marital status.

30.

1,2,…

32.

1.4

35.

0, 1, 2, 3, 4, …

37.

0.0485

39.

0.0214

41.

$$X =$$ the number of U.S. teens who die from motor vehicle injuries per day.

43.

0, 1, 2, 3, 4, ...

45.

No

48.

1. 50.
1. 53.

$$X =$$ the number of patients calling in claiming to have the flu, who actually have the flu.

55.

0.0165

57.

1. 59.

4. 4.43

4

63.

• 65.
1. 67.
1. 69.
1. 71.
1. 73.
1. Figure $$\PageIndex{4}$$
2. 75.
1. 77.
1. 79.

0, 1, 2, and 3

1. 82.
1. 84.

Let $$X =$$ the number of defective bulbs in a string.

• Using the binomial distribution:
• The Poisson approximation is very good—the difference between the probabilities is only $$0.0026$$.

86.

1. 88.
1. 90.
1. 92.
1. 94.

4

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