Question

Which of the following are valid probability distribution functions? (Hint: The P values have to follow...

  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

Homework Answers

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

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