For Exercises 3-17 to 3-21, verify that the following

Chapter 3, Problem 17E

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QUESTION:

For Exercises 3-17 to 3-21, verify that the following functions are probability mass functions, and determine the requested probabilities.

(a) \(P(X \leq 2)\)         (b) \(P(X>-2)\)         (c) \(P(-1 \leq x \leq 1)\)         (d) \(P(X \leq-1\) or \(X=2 \text { ) }\)

Equation transcription:

P(-1x1)

Text transcription:

P(X leq 2)

P(X>-2)

P(-1 leq x leq 1)

P(X leq-1

X=2 text { ) }

Questions & Answers

QUESTION:

For Exercises 3-17 to 3-21, verify that the following functions are probability mass functions, and determine the requested probabilities.

(a) \(P(X \leq 2)\)         (b) \(P(X>-2)\)         (c) \(P(-1 \leq x \leq 1)\)         (d) \(P(X \leq-1\) or \(X=2 \text { ) }\)

Equation transcription:

P(-1x1)

Text transcription:

P(X leq 2)

P(X>-2)

P(-1 leq x leq 1)

P(X leq-1

X=2 text { ) }

ANSWER:

Solution

Step 1 of 5

We have to verify the given function is a probability mass function or not

And we have to find the following probabilities

Here each probability value is greater than zero ()

And the total probability is equal to one ()

Hence the given function is a probability mass function


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