Which of the following are valid probability distributions f

Which of the following are valid probability distributions for a discrete random variable\'? Check all that apply. A. 1/12, 1/12, 1/12, 1/12, 1/6 1/12, 1/12, 1/12, 1/12, 1/6 B. 1/5, 1/5, 1/5, 1/5, 1/5 C. -1/2, -1/3, -1/4, -1/5, 137/60 D. 1/6, 1/5, 1/4, 1/3 E. 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/128

Solution

For a valid probability density function the total sum of probabilities must be 1

so here

option A and B are correct since the probabilites sum up to 1

Option C is not correct since we cannot have negative probabilites

option D is not since 1/3+1/4+1/5+1/6 = 0.95

option E is not since 1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 0.992

So the answers are A and B