The probability distribution for a discrete random variable is not valid for options B and C.
We have given the probability distribution for a discrete random variable where the sum of all possible events needs to be 1.
What is probability?
Probability refers to the occurrence of a random event. The probability of an event is always is between 0 and 1. The probability distribution is a basic theory of probability where we learn the possibility of outcomes for random events.
A. 1/5,1/10 ,1/10 ,1/10 ,1/5 ,1/10 ,1/10 , 1/10
= \(\frac{1}{5} +\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
= \(\frac{6}{10} +\frac{2}{5}\)
= 1
Since the sum of all possible events is 1. So, it can be valid probability distribution for a discrete random variable.
B. 1/3,1/4,1/5,1/6
= \(\frac{1}{3} +\frac{1}{4} +\frac{1}{5} +\frac{1}{6} \\\)
= \(\frac{3}{6} +\frac{9}{20} \\=0.95\)
Since the sum of all possible events is 1. So, it can be valid probability distribution for a discrete random variable.
C. 1/2,1/4 ,1/8 ,1/16 ,1/32 ,1/64 ,1/128 ,1/128
= \(\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16}+\frac{1}{32}+\frac{1}{64} +\frac{1}{128} +\frac{1}{128}\)
= 0.98
Since the sum of all possible events is 1. So, it can be valid probability distribution for a discrete random variable.
D. -1/2, -1/3, -1/4, -1/5, 137/60
= \(\frac{-1}{2} +\frac{-1}{3}+\frac{-1}{4}+\frac{-1}{5}+\frac{137}{60}\\\)
= 1
Since the sum of all possible events is 1. So, it can be valid probability distribution for a discrete random variable.
E. 1/6, 1/6, 1/6, 1/6, 1/6, 1/6
= \(\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} \\\)
= 1
Since the sum of all possible events is 1. So, it can be valid probability distribution for a discrete random variable.
Hence, options B and C are not valid probability distributions for a discrete random variable.
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