Question

Which of the following is a valid probability distribution for a discrete random variable? Check all that apply.

A. 0.21, 0.16, -.08, 0.05, 0.04, 0.03, -0.24, 0.12, 0.21, 0.18, 0.32
B. 0.18, 0.12, 0.03, 0.08, 0.21, 0.04, 0.05, 0.16, 0.13
C. 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1
D. 0.1, 0.2, 0.3, 0.4
E. 1.0

I know that they must add up to 1, but I need to know if it can be E.

Answer 1

No it cannot, because it is the number in and of itself, not an equation that adds up to one. Hope it helped!

Answer 2

The correct options are B, D and E.

Explanation:

The basic requirement for a valid probability distribution for a discrete random variable are

1. All probability must between 0 and 1.

2. Sum of all the probabilities must be 1.

In option A,

0.21, 0.16, -0.08, 0.05, 0.04, 0.03, -0.24, 0.12, 0.21, 0.18, 0.32

The probability of an event can't be negative. So, option A is incorrect.

In option B,

0.18, 0.12, 0.03, 0.08, 0.21, 0.04, 0.05, 0.16, 0.13

All values lie between 0 and 1. Sum of all probabilities is

`0.18+0.12+0.03+0.08+0.21+0.04+0.05+0.16+0.13=1`

Sum of probability is 1. So, option B is correct.

In option C,

0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1

All values lie between 0 and 1. Sum of all probabilities is 1.1, which is more than 1.

So, option C is incorrect.

In option D,

0.1, 0.2, 0.3, 0.4

In option D,

0.1, 0.2, 0.3, 0.4

All values lie between 0 and 1. Sum of all probabilities is 1.

So, option D is correct.

In option E,

1.0

The probability of an event is 1 if it is certain to happen.Sum of all probabilities is 1.

So, option E is correct.

Therefore the correct options are B, D and E.