Question

1. Which of the following are valid probability distribution functions? (Hint: The P values have to follow the rules previously given for probabilities.)

x	P(x)
5	0.6
6	0.8
7	– 0.4

x	P(x)
1	.1
2	.2
3	.3
4	.4

x	0	1	2	3	4
P(x)	1/6	1/6	1/6	1/6	1/6

Answer 1

1) The given probability distribution is:

x	P(x)
5	0.6
6	0.8
7	– 0.4

This is NOT a probability distribution, since for P(x) to be a probability, it should be > 0 for all values of x However, in the above table, it takes value of -0.4 for x=7

2) The second probability distribution is:

x	P(x)
1	0.1
2	0.2
3	0.3
4	0.4

This is a probability distribution, since and P(x) >= 0 x in {1, 2, 3, 4) and 0 elsewhere

3) The last probability distribution is:

x	0	1	2	3	4
P(x)	1/6	1/6	1/6	1/6	1/6

Though P(x) >= 0 x, . Hence, this is not a probability distribution