Question

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

A. (0.01) 11, (0.01) 12, (0.01) 13, ...
B. 0.35, 0.18, 0.21, 0.06, 0.17, 0.03
C. 0.16, 0.193, 0.222, 0.233, 0.067, 0.125
D. 0.16, 0.12, 0.02, 0.08, 0.22, 0.05, 0.15, 0.02, 0.18
E. 0.12, -0.02, 0.18, 0.08, 0.15, 0.05, 0.16, 0.27, 0.02, 0.36, -0.15, -0.22

Answer 1

for one thing a probability cannot be negative

Answer 2

When you say "probability distributions for a discrete random variable" we should expect to see ordered pairs of values and probabilities. Each probability is always between zero and 1 and the sum of all probabilities equals 1.

Answer 3

good point

Answer 4

Can you multiply?

Answer 5

So one discrete random variable generator is a six-sided die. It's distribution looks like:
(x,p)::(1,1/6),(2,1/6),(3,1/6),(4,1/6),(5,1/6),(6,1/6)

Answer 6

I might also have a trick die for rolling more sixes than usual:
(x,p)::(1,0.1),(2,0.1),(3,0.1),(4,0.1),(5,0.1),(6, 0.5)

Answer 7

But I couldn't have a distribution where the probabilities didn't sum to 1, or any result was anti-possible or super-possible (I just made up those terms).

Answer 8

Okay.

Answer 9

With the lists you have in your question, I can't really tell what are x's and what are p's.

Answer 10

So C and E are possible probability vectors because they sum to 1 and are never <0 or >1. They are not communicating the x values.

Answer 11

Okay.

Answer 12

It is possible that the "x values" are things like "red, green, blue, purple..." so this is maybe fine. I like to know what it is that has a 0.16 chance of, but that's just me.