Suppose that an experimenter tossed three balanced coins. He defined ?1, to denote the number of heads and ?2, is to denote the amount of money won on a daily lotto bet in South Africa in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. If the first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear, the R1 (that is, win −R1) is lost. Find i) the joint probability function of ?1and ?2. (5) ii) the probability that less than 3 heads will occur and the student will win R1 or less.
Suppose that an experimenter tossed three balanced coins. He defined ?1, to denote the number of heads and ?2, is to denote the amount of money won on a daily lotto bet in South Africa in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. If the first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear, the R1 (that is, win −R1) is lost. Find i) the joint probability function of ?1and ?2. (5) ii) the probability that less than 3 heads will occur and the student will win R1 or less.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 72CR
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Question
Suppose that an experimenter tossed three balanced coins. He defined ?1, to denote the
number of heads and ?2, is to denote the amount of money won on a daily lotto bet in South
Africa in the following manner. If the first head occurs on the first toss, R1 (one rand) is won. If
the first head occurs on toss 2 or on toss 3, R2 or R3 is won respectively. If no heads appear,
the R1 (that is, win −R1) is lost.
Find
i) the joint probability function of ?1and ?2. (5)
ii) the probability that less than 3 heads will occur and the student will win R1 or less. (2)
QUESTION 2 [19]
a) Suppose that random variables ?1 and ?2 have exponential distribution with expec
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