The valid probability distributions for a discrete random variable are :
Option D
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
Let us tackle the problem.
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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.
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Option A :
[tex]0.2 + 0.35 + 0.15 + 0.25 = 0.95 \ne 1[/tex] ⤬
This is not the valid probability distributions for a discrete random variable because the sum of all the probability of distributions is not equal to 1.
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Option B :
[tex]-0.2 + (-0.1) + 0.4 + 0.3 = 0.4 \ne 1[/tex] ⤬
This is not the valid probability distributions for a discrete random variable because the sum of all the probability of distributions is not equal to 1.
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Option C :
[tex]0.4 + 1.05 + 0.02 + 0.35 = 1.82 \ne 1[/tex] ⤬
This is not the valid probability distributions for a discrete random variable because the sum of all the probability of distributions is not equal to 1.
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Option D :
[tex]0.4 + 0.15 + 0.25 + 0.2 = 1[/tex] ✔
This is the valid probability distributions for a discrete random variable
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die