Which of the following is not a valid probability distribution for a discrete random variable? check all that apply.

a. 1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10

b. 1/3,1/4 ,1/5 ,1/6

c. 1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128

d. -1/2, -1/3, -1/4, -1/5, 137/60

e. 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

Only Options 'B' and 'D' are not valid probability distribution for a discrete random variable.

Step-by-step explanation:

Since we have given the probability distribution for a discrete random varible.

As we know that the sum of all possible events needs to be 1.

And probability is always between 0 and 1

It can't be negative.

So, we will done by options:

A.1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10

And it is between 0 and 1.

So, it can be valid probability distribution for a discrete random variables.

B.1/3,1/4 ,1/5 ,1/6

So, it can't be valid probability distribution for a discrete random variables.

C.1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128

So, it can be valid probability distribution for a discrete random variable.

D.-1/2, -1/3, -1/4, -1/5, 137/60

It can't be valid probability distribution as it is not between 0 and 1, it has values less than 1.

E.1/6, 1/6, 1/6, 1/6, 1/6, 1/6

so, it can be valid probability distribution for a discrete random variable.

Hence, only Options 'B' and 'D' are not valid probability distribution for a discrete random variable.