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Chapter 5: Q 5.137. (page 230)

Dice. The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows

Part (a) Find and interpret the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10

Part (c) Construct a probability histogram for the random variable, locate the mean: and show one, two, and three standard deviation intervals.

Short Answer

Expert verified

Part (a) 7

Part (b) 2.42

Part (c)

Step by step solution

01

Part (a) Step 1. Given information. 

Consider the following table of data. When two Balanced dice are rolled, the random variable Y is the sum of the dice.

02

Part (a) Step 2. The random variable's average.

渭=鈭�y路P(Y=y)渭=21/36+3(1/18)+......121/36渭=0+0.056+0.167+.....0.333渭=7

Two balanced dice are rolled, the mean of the sum of the dice is 7

03

Part (b) Step 1.The random variable's standard deviation:

Standard deviation

蟽=鈭�x2P(X=x)-渭2蟽=41/36+91/18.....1441/36-72蟽=5.833蟽=2.415

As a result, standard deviation = 2.42

04

Part (c) Step 1.  The mean, one, two, and three standard deviation intervals on the probability histogram graph of the random variable.

We have 渭and 蟽from sections a and b.

渭-蟽,渭+蟽=7-2.42,7+2.42=4.58,9.41渭-2蟽,渭+2蟽=7-2(2.42),7+2(2.42)=(2.17,11.83)渭-3蟽,渭+3蟽=7-3(2.42),7+3(2.42)=(-0.25,14.25)

Draw the probability histogram graph:

The probability histogram graph of the random variable with the mean and one, two, and three standard deviation intervals is shown above.

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Most popular questions from this chapter

Playing Cards. An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs- with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is

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