A game consists of tossing a fair coin 3 times. Let random variable W denote the number of heads obtained. We also let random variable Z denote the winnings earned in a single play of a game with the following rules, the outcomes of the 3 spins of the coin. • player wins $1 if first Head occurs on the first toss • player wins $2 if first Head occurs on the second toss • player wins $3 if first Head occurs on the third toss • player loses $1 if no Head occurs after 3 tosses. (a) What is the range of W (b) What is the range of Z (c) What is the joint PMF of pwz(w, z) (d) Are W and Z independent?

A game consists of tossing a fair coin 3 times. Let random variable W denote the number of heads obtained. We also let random variable Z denote the winnings earned in a single play of a game with the following rules, the outcomes of the 3 spins of the coin. • player wins $1 if first Head occurs on the first toss • player wins $2 if first Head occurs on the second toss • player wins $3 if first Head occurs on the third toss • player loses $1 if no Head occurs after 3 tosses. (a) What is the range of W (b) What is the range of Z (c) What is the joint PMF of pwz(w, z) (d) Are W and Z independent?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...

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