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Chapter 5: Q 5.106 (page 224)

Fill in the blank.

For a discrete random variable, the sum of the probabilities of its possible values equals ____.

Short Answer

Expert verified

The sum of the probabilities of all discrete random variables equals 1.

Step by step solution

01

Given information

Take :

"The total of the probability of all possible values for a discrete random variable is equal to ___."

02

Solution

The total probability of all possible values for a discrete random variable is always 1. Consider the following random variable X, which can take one of two values: 1 or 2, with

P(1)=0.3andP(2)=0.7.P ( 1 ) = 0.3 and P ( 2 ) = 0.7.

in this case.

P(1)+P(2)=1

Because total likelihood resembles that one of the outcomes will occur, which is always true, the sum of the probabilities will always equal 1.

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Suppose that A, B, C are three events that cannot all occur simultaneously. Does this condition necessarily imply that A, B, and C are mutually exclusive ? Justify your answer and illustrate it with a venn diagram.

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