Respuesta :
Answer: 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
[tex]\frac{1}{5}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\\\\=\frac{2}{5}+\frac{6}{10}\\\\=\frac{2}{5}+\frac{3}{5}\\\\=1[/tex]
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
[tex]\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=0.95\neq 1[/tex]
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
[tex]\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{28}\\\\=1[/tex]
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
[tex]\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\\\\=1[/tex]
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.
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
= [tex]\frac{1}{5} +\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}[/tex]
= [tex]\frac{6}{10} +\frac{2}{5}[/tex]
= 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
= [tex]\frac{1}{3} +\frac{1}{4} +\frac{1}{5} +\frac{1}{6} \\[/tex]
= [tex]\frac{3}{6} +\frac{9}{20} \\=0.95[/tex]
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
= [tex]\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16}+\frac{1}{32}+\frac{1}{64} +\frac{1}{128} +\frac{1}{128}[/tex]
= 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
= [tex]\frac{-1}{2} +\frac{-1}{3}+\frac{-1}{4}+\frac{-1}{5}+\frac{137}{60}\\[/tex]
= 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
= [tex]\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} +\frac{1}{6} \\[/tex]
= 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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