Question

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

Answer 1

Answer:

Option B and D are correct.

Step-by-step explanation:

We know that Sum of the probability distribution of a discrete random variable is equal to 1.

using this result we check which is not valid probability distribution.

Option A).

Sum of Probability Distribution

$=\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{2+1+1+1+2+1+1+1}{10}=\frac{10}{10}=1$

So, This is valid Probability distribution.

Option B).

Sum of Probability Distribution

$=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{20+15+12+10+}{60}=\frac{57}{10}\neq1$

So, This is not a valid Probability distribution.

Option C).

Sum of Probability Distribution

$=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{128}=\frac{64+32+16+8+4+2+1+1}{128}=\frac{128}{128}=1$

So, This is valid Probability distribution.

Option D).

Given Probability Distribution has negative probability which is not possible.

So, This is not a valid Probability distribution.

Option E).

Sum of Probability Distribution

$=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1+1+1+1+1+1}{6}=\frac{6}{6}=1$

So, This is valid Probability distribution.

Therefore, Option B and D are correct.