4.75 Use the central limit theorem to verify the following results. (a) The probability of getting r or more sixes in one throw of 6r fair dice tends to 1/2 as r.
4.75 Use the central limit theorem to verify the following results. (a) The probability of getting r or more sixes in one throw of 6r fair dice tends to 1/2 as r.
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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 8CR
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Question
Question number 4.75
![(a) What is, in Example 3.3, a good approximation for the probability
that the profit of Joe and his brother will be $100 or more after 52
weeks?
(b) What is a good approximation for the probability that more than 80
rolls are required when you roll a fair die until the total sum exceeds
300?
4.74 Let X₁, X2,... be a sequence of independent random variables each
having the same distribution with expected value μ and standard devi-
ation G. Show that P(1/(X₁ + ... + Xn) − µl > c) ~2 [1- (W/M)]
for n large.
DEN
4.75 Use the central limit theorem to verify the following results.
d bamislo 21m
(a) The probability of getting r or more sixes in one throw of 6r fair dice
tends to as r.
2 100 odt blod
OH
(b) e¯”(1 + m + 2 + ... + m) tends to 1/2
2!
as n →∞.
4.76 An insurance company has 20,000 policyholders. The amount claimed
yearly by a policyholder has an expected value of $150 and a standard
deviation of $750. Give an approximation for the probability that the total
amount claimed in the coming year will be larger than 3.3 million dollars.
4.77 In the 52 drawings of the 6/45 lottery in Orange Country last year, an
even
un 163 times and an odd number 150 times. Does](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02433631-7a65-4f58-bcbc-1ca9258e00c4%2F3da3b4b4-3f62-4104-ab5d-9c321d9913b7%2Fbliuea8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) What is, in Example 3.3, a good approximation for the probability
that the profit of Joe and his brother will be $100 or more after 52
weeks?
(b) What is a good approximation for the probability that more than 80
rolls are required when you roll a fair die until the total sum exceeds
300?
4.74 Let X₁, X2,... be a sequence of independent random variables each
having the same distribution with expected value μ and standard devi-
ation G. Show that P(1/(X₁ + ... + Xn) − µl > c) ~2 [1- (W/M)]
for n large.
DEN
4.75 Use the central limit theorem to verify the following results.
d bamislo 21m
(a) The probability of getting r or more sixes in one throw of 6r fair dice
tends to as r.
2 100 odt blod
OH
(b) e¯”(1 + m + 2 + ... + m) tends to 1/2
2!
as n →∞.
4.76 An insurance company has 20,000 policyholders. The amount claimed
yearly by a policyholder has an expected value of $150 and a standard
deviation of $750. Give an approximation for the probability that the total
amount claimed in the coming year will be larger than 3.3 million dollars.
4.77 In the 52 drawings of the 6/45 lottery in Orange Country last year, an
even
un 163 times and an odd number 150 times. Does
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