For the questions below, please show the derivation of the distributions step by step. (a) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let (b) Y = (X₁ + X₂ + X₁ + X₂)² + (X₁ + X₁ + X₁ + Xg)². Obtain the c value so that the random variable cY has a x² distribution. Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable
For the questions below, please show the derivation of the distributions step by step. (a) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let (b) Y = (X₁ + X₂ + X₁ + X₂)² + (X₁ + X₁ + X₁ + Xg)². Obtain the c value so that the random variable cY has a x² distribution. Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:For the questions below, please show the derivation of the distributions step by step.
(a)
Suppose that the random variables X₁,..., X, form a random sample from a
standard normal distribution. Let
(b)
Y = (X₁ + X₂ + X₂ + X₁)² + (X₂ + X6 + X₁ + X)².
Obtain the c value so that the random variable cY has a x² distribution.
Suppose that X₁,..., X, are independent and identically distributed random
variables from a standard normal distribution. Obtain the value of d so
that the random variable
has at distribution.
d(x₁ - + X₂ + X₂)
(X₂²+X₂²+X₂²
X,²)/²
(c)
If S and S are the variance for the sample of independent random variables
with size n₁ = 6 and n₂ =10, taken from a Normal distribution with common
variance, calculate the value of e so that P(S²/S2 <e)=0.05.
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