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# Probability distribution function

1. When two balanced dice are rolled, 36 equally likely outcomes are possible. Let X denote the smaller of the two numbers. If both dice come up with the same number, then X equals that common value. Find the probability distribution of X. Leave your probability in fraction form.
a. x P(X=x)
1 5/18
2 2/9
3 1/6
4 1/9
5 1/18
6 0

b. x P(X=x)
1 11/36
2 1/4
3 7/36
4 5/36
5 1/12
6 1/36

c. x P(X=x)
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
6 1/6

d. x P(X=x)
1 5/18
2 1/4
3 7/36
4 5/36
5 1/9
6 1/36

2. The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table below. Find the mean of the random variable.

x P(X=x)
0 0.4096
1 0.4096
2 0.1536
3 0.0256
4 0.0016

a. 2.00

b. 1.21

c. 0.80

d. 0.70

3. The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table below. Find the standard deviation of the random variable.

x P(X=x)
0 0.2401
1 0.4116
2 0.2646
3 0.0756
4 0.0081

a. 1.51

b. 1.06

c. 0.84

d. 0.92

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