scheme of random number generator is described as follows. First, one generates a normal random number with mean 0 and variance 16, a uniform random number on [0,24], then a geometric random number of parameter p = 0.25 (each independently). Then we define the random number to be the average of these three numbers. 30 random numbers are generated with the scheme above, denoted as {X₂}³º₁. Estimate/approximate the probability that the average 1 X is deviated from μ = E[X₁] by a distance of more than 0.2 using: (a) Chebyshev's inequality; (b) central limit theorem. 130 k=1*
scheme of random number generator is described as follows. First, one generates a normal random number with mean 0 and variance 16, a uniform random number on [0,24], then a geometric random number of parameter p = 0.25 (each independently). Then we define the random number to be the average of these three numbers. 30 random numbers are generated with the scheme above, denoted as {X₂}³º₁. Estimate/approximate the probability that the average 1 X is deviated from μ = E[X₁] by a distance of more than 0.2 using: (a) Chebyshev's inequality; (b) central limit theorem. 130 k=1*
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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![A scheme of random number generator is described as follows. First, one
generates a normal random number with mean 0 and variance 16, a uniform random number
on [0,24], then a geometric random number of parameter p = 0.25 (each independently).
Then we define the random number to be the average of these three numbers. 30 random
numbers are generated with the scheme above, denoted as {X}31. Estimate/approximate
the probability that the average 1 X is deviated from μ = E[X₁] by a distance of more
than 0.2 using: (a) Chebyshev's inequality; (b) central limit theorem.
k=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd94c6fe5-0a79-4b34-8240-29323f6fd175%2Fee854f8e-62ec-4780-8b59-0f95c69919f8%2F2dpr10w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A scheme of random number generator is described as follows. First, one
generates a normal random number with mean 0 and variance 16, a uniform random number
on [0,24], then a geometric random number of parameter p = 0.25 (each independently).
Then we define the random number to be the average of these three numbers. 30 random
numbers are generated with the scheme above, denoted as {X}31. Estimate/approximate
the probability that the average 1 X is deviated from μ = E[X₁] by a distance of more
than 0.2 using: (a) Chebyshev's inequality; (b) central limit theorem.
k=1
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