The valid probability distributions for a discrete random variable are :
Option A , D , and E
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
Let us tackle the problem.
In a discrete random variable , the sum of all the probability of distributions must equal to 1. The minimum value of probability is 0 and the maximum value of probability is 1.
Option A :
[tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{6}{6} = 1[/tex] ✔
This is the valid probability distributions for a discrete random variable
Option B :
[tex]\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{19}{20} \ne 1[/tex] ⤬
This is not the valid probability distributions for a discrete random variable
Option C :
[tex]-\frac{1}{2} - \frac{1}{3} - \frac{1}{4} - \frac{1}{5} + \frac{137}{60} = 1[/tex] ⤬
Although the sum is 1 but this is still not the valid probability distributions for a discrete random variable because probability cannot have negative values.
Option D :
[tex]\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{128} = 1[/tex] ✔
This is the valid probability distributions for a discrete random variable
Option E :
[tex]\frac{1}{5} + \frac{1}{10} + \frac{1}{10} +...+ \frac{1}{10} = 1[/tex] ✔
This is the valid probability distributions for a discrete random variable
Learn more
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die
