Q1. Let X and S² be the mean and the variance of a random sample of size n = 16 from a distributionn(u, o²). Find the constant c such that P4(X – µ)·c <= 0.95.SQ2. Let {X1, X2, .Xn} be an independent random sample from a Poisson(A) distribution, where...A is an unknown parameter. Suppose that the sample size n is large.(a) Find a pivotal variable in terms of X and the parameter A using normal approximation basedon the Central Limit Theorem.(b) Derive an approximate (1– a) confidence interval for A using the pivotal variable found in part(a).(c) Construct a 95% confidence interval for A if X = 1.5 and S2= 4 from a random sample ofsize n = 36.

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Description: Q1. Let X and S² be the mean and the variance of a random sample of size n = 16 from a distributionn(u, o²). Find the constant c such that P4(X – µ)·c <= 0.95.SQ2. Let {X1, X2, .Xn} be an independent random sample from a Poisson(A) distribution, whe

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Q1. Let X and S² be the mean and the variance of a random sample of size n = 16 from a distribution 4(X – µ) c < n(µ, o²). Find the constant c such that P = 0.95. S

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Q1. Let X and S² be the mean and the variance of a random sample of size n = 16 from a distribution
n(u, o²). Find the constant c such that P
4(X – µ)
·c <
= 0.95.
S
Q2. Let {X1, X2, .
Xn} be an independent random sample from a Poisson(A) distribution, where
...
A is an unknown parameter. Suppose that the sample size n is large.
(a) Find a pivotal variable in terms of X and the parameter A using normal approximation based
on the Central Limit Theorem.
(b) Derive an approximate (1– a) confidence interval for A using the pivotal variable found in part
(a).
(c) Construct a 95% confidence interval for A if X = 1.5 and S2
= 4 from a random sample of
size n = 36.

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