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(a) The friendly instructor went to visit the casino to play with a biased coin, where the head shows up with probability p = }. Let T be the number of games needed until the head shows up 125 times. Describe the random variable T (e.g., binomial, Poisson) with its parameter. (b) T≤ 675) (d) (c) Let X₁,... X100 be independent exponential random vari- ables with mean = 1. Let X = X₁+...+X100 Describe the random variable X with its parameter. = 100 Use the central limit theorem to approximate P(525 < X ≤ 0.99) Use the central limit theorem to approximate P(0.985 <

(a) The friendly instructor went to visit the casino to play with a biased coin, where the head shows up with probability p = }. Let T be the number of games needed until the head shows up 125 times. Describe the random variable T (e.g., binomial, Poisson) with its parameter. (b) T≤ 675) (d) (c) Let X₁,... X100 be independent exponential random vari- ables with mean = 1. Let X = X₁+...+X100 Describe the random variable X with its parameter. = 100 Use the central limit theorem to approximate P(525 < X ≤ 0.99) Use the central limit theorem to approximate P(0.985 <

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Central limit theorem

8. (a) (b) The friendly instructor went to visit the casino to play with a biased coin, where the head shows up with probability p= . Let T be the number of games needed until the head shows up 125 times. Describe the random variable T (e.g., binomial, Poisson) with its parameter. (d) T≤ 675) (c) Let X₁,... X100 be independent exponential random vari- ables with mean 1. Let X = X₁+...+X100. Describe the random variable X with its parameter. 100 Use the central limit theorem to approximate P(525 < X < 0.99) = Use the central limit theorem to approximate P(0.985 <
Transcribed Image Text:8. (a) (b) The friendly instructor went to visit the casino to play with a biased coin, where the head shows up with probability p= . Let T be the number of games needed until the head shows up 125 times. Describe the random variable T (e.g., binomial, Poisson) with its parameter. (d) T≤ 675) (c) Let X₁,... X100 be independent exponential random vari- ables with mean 1. Let X = X₁+...+X100. Describe the random variable X with its parameter. 100 Use the central limit theorem to approximate P(525 < X < 0.99) = Use the central limit theorem to approximate P(0.985 <
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