Suppose that in Exercise 2.4-1, X = 1 if a red ball is

Chapter 2, Problem 2E

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QUESTION:

Problem 2E

Suppose that in Exercise 2.4-1, X = 1 if a red ball is drawn and X = −1 if a white ball is drawn. Give the pmf, mean, and variance of X.

References Exercise 2.4-1

An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X = 1 if a red ball is drawn, and let X = 0 if a white ball is drawn. Give the pmf, mean, and variance of X.

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QUESTION:

Problem 2E

Suppose that in Exercise 2.4-1, X = 1 if a red ball is drawn and X = −1 if a white ball is drawn. Give the pmf, mean, and variance of X.

References Exercise 2.4-1

An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X = 1 if a red ball is drawn, and let X = 0 if a white ball is drawn. Give the pmf, mean, and variance of X.

ANSWER:

Answer :

Step 1 of 1:

From the given information an urn contains 7 red and 11 white balls.

The total balls is 7+11 = 18 balls.

X=1 IF red ball is drawn.

So P(X=1) =

x=-1 if white ball is drawn.

So P(x=-1) =

Then the pmf is

mean :

Now we need to find the mean.

We know that

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