Solved: For Exercises 3-17 to 3-21, verify that the

Chapter 3, Problem 20E

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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.

\(f(x)=(3 / 4)(1 / 4)^{x}, x=0,1,2, \ldots\)
(a) \(P(X=2)\)
(b) \(P(X \leq 2)\)
(c) \(P(X>2)\)
(d) \(P(X \geq 1)
)

Equation transcription:

Text transcription:

f(x)=(3 / 4)(1 / 4)^{x}, x=0,1,2, ldots

P(X=2)

P(X leq 2)

P(X>2)

P(X geq 1)

Questions & Answers

QUESTION:

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

\(f(x)=(3 / 4)(1 / 4)^{x}, x=0,1,2, \ldots\)
(a) \(P(X=2)\)
(b) \(P(X \leq 2)\)
(c) \(P(X>2)\)
(d) \(P(X \geq 1)
)

Equation transcription:

Text transcription:

f(x)=(3 / 4)(1 / 4)^{x}, x=0,1,2, ldots

P(X=2)

P(X leq 2)

P(X>2)

P(X geq 1)

ANSWER:

Solution:

Step 1 of 3:

We have to verify the given function is a probability mass function, also we have to find the following probabilities.

                                       , x=0, 1, 2,...

  1. P(X=2)
  2. P(X
  3. P(X>2)
  4. P(X


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