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Let the random variable X have the pdf f (x) =2(1 ? x), 0

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 9E Chapter 3.1

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 9E

Problem 9E

Let the random variable X have the pdf f (x) =2(1 − x), 0 ≤ x ≤ 1, zero elsewhere.

(a) Sketch the graph of this pdf.

(b) Determine and sketch the graph of the cdf of X.

(c) Find (i) P(0 ≤ X ≤ 1/2), (ii) P(1/4 ≤ X ≤ 3/4),

(iii) P(X = 3/4), and (iv) P(X ≥ 3/4).

Step-by-Step Solution:

Answer :

Step 1 of 3 :

Given,

The random X have the probability density function f(x) = 2(1 - x) , 01

  1. The claim is to find the pdf and sketch the graph.

     Where, the limits are lies between  0 to 1

Let  us consider the x = 0, 0.25 , 0.50, 0.75 and 1

Then the pdf is

x

f(x) = 2(1 - x)

0

2

0.25

1.5

0.5

1

0.75

.5

1

0

From Excel

> insert the data in excel sheet

> select the data

> go to insert option

> select the chart


Step 2 of 3

Chapter 3.1, Problem 9E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Let the random variable X have the pdf f (x) =2(1 ? x), 0