ONLY PART 1 EXERCISE 5Suppose that X1,·, Xm and Y1, ., Yn are two samples, with X; -between the sample means, X – Ý, is then a linear combination of m +n normal random variables. All the randomvariables are independent. Answer the following questions:Ν(μ1, σι) and YN(u2, 02). The differencea. Use moment generating functions to show that Xvariance of this distribution.Y follows a normal distribution. Find the mean and-b. Suppose o = 2, o% = 2.5, and m = n. Find the sample size n so that X - Ý will be within one unit of µiwith probability 0.95.

We have to use moment generating function to prove that difference between sample mean of two normal…

EXERCISE 5 Suppose that X1,·,Xm and Y1, , Yn are two samples, with X; between the sample means, X – Ỹ, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: N(u1,01) and Y; ~ N(u2, 02). The difference a. Use moment generating functions to show that X - Ý follows a normal distribution. Find the mean and variance of this distribution. b. Suppose oi = 2, o = 2.5, and m = n. Find the sample size n so that X - Y will be within one unit of µi – µ2 with probability 0.95.

EXERCISE 5 Suppose that X1,·,Xm and Y1, , Yn are two samples, with X; between the sample means, X – Ỹ, is then a linear combination of m +n normal random variables. All the random variables are independent. Answer the following questions: N(u1,01) and Y; ~ N(u2, 02). The difference a. Use moment generating functions to show that X - Ý follows a normal distribution. Find the mean and variance of this distribution. b. Suppose oi = 2, o = 2.5, and m = n. Find the sample size n so that X - Y will be within one unit of µi – µ2 with probability 0.95.

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.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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