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Statistics / Probability and Statistical Inference 9 / Chapter 5.4 / Problem 5.4-1

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

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Let X1, X2, X3 be a random sample of size 3 from the distribution with pmf f(x) = 1/4, x

Chapter 5, Problem 5.4-1

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QUESTION:

Let X1, X2, X3 be a random sample of size 3 from the distribution with pmf f(x) = 1/4, x = 1, 2, 3, 4. For example, observe three independent rolls of a fair four-sided die. (a) Find the pmf of Y = X1 + X2 + X3. (b) Sketch a bar graph of the pmf of Y.

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QUESTION:

Let X1, X2, X3 be a random sample of size 3 from the distribution with pmf f(x) = 1/4, x = 1, 2, 3, 4. For example, observe three independent rolls of a fair four-sided die. (a) Find the pmf of Y = X1 + X2 + X3. (b) Sketch a bar graph of the pmf of Y.

ANSWER:

Problem 5.4.1

Let be a random sample of size 3 from the distribution with pmf f(x) = 1/4, x = 1, 2, 3, 4. For example, observe three independent rolls of a fair four-sided die.

(a) Find the pmf of .

(b) Sketch a bar graph of the pmf of Y.

Step by Step Solution

Step 1 of 3

(a)

Let and are independents and each of and can take the values.

So, the total possible arrangements of and is .

Since,

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