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Flip n = 8 fair coins and remove all that came up heads.

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

Solution for problem 19E Chapter 5.3

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 19E

Problem 19E

Flip n = 8 fair coins and remove all that came up heads. Flip the remaining coins (that came up tails) and remove the heads again. Continue flipping the remaining coins until each has come up heads. We shall find the pmf of Y, the number of trials needed. Let Xi equal the number of flips required to observe heads on coin

i, i = 1, 2, . . . , 8. Then Y = max(X1,X2, . . . ,X8).

(a) Show that P(Y y) = [1 − (1/2)y]8.

(b) Show that the pmf of Y is defined by P(Y = y) =[1 − (1/2)y]8 − [1 − (1/2)y−1]8, y = 1, 2, . . . .

(c) Use a computer algebra system such as Maple or Mathematica to show that the mean of Y is E(Y) =13,315,424/3,011,805 = 4.421.

(d) What happens to the expected value of Y as the number of coins is doubled?

Step-by-Step Solution:

Step 1 of 8

We assume that the coin tosses  are independent.

We have one chance out of 2 to toss heads:

Step 2 of 8

Chapter 5.3, Problem 19E is Solved
Step 3 of 8

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

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Flip n = 8 fair coins and remove all that came up heads.