Part B Urgently 1. (a) Let X be a continuous random variable with pdfSc(1 – x)? – b 0 <¤< 2fx(x) =otherwise,for constants c>0 and b.(i) Show that b cannot be positive.(ii) Show that c =(1+ 26).Let b = -:(iii) Find Fx(1), where Fx is the cdf of X.(iv) Find P(X = 0).(v) Find E[X].(b) Let X1,..., Xn be independent Ber(0) random variables and letY = X1 +...+ Xn.(i) Calculate the moment generating function of X1.(ii) Hence find the moment generating function of Y.(iii) Hence calculate the expectation and variance of Y.(iv) Write down the name of the distribution of Y.(c) A car manufacturer claims that the fuel efficiency of its vehiclesmeets a regulatory standard of 47 miles per gallon (mpg). Toassess this claim, the fuel efficiencies of a simple random sampleof 15 cars were measured. The mean of the 15 measurements was= 46.75 mpg and their standard deviation was s 0.72 mpg.y =Assume that the measurements follow a Normal distribution.(i) Conduct a test of size 5% of the null hypothesis that thepopulation mean efficiency is 47 mpg against the alternativehypothesis that the population mean efficiency is less than 47mpg. State clearly your test statistic, its null distribution, thecritical region, and your conclusion about the manufacturer'sclaim.(ii) Compute an equal-tailed 95% confidence interval for thepopulation mean efficiency.

Answered: Image /qna-images/answer/4f8855d5-fa13-44f6-984f-5fbd2babacef.jpg

(b) Let X1,..., X, be independent Ber(0) random variables and let Y = X1 +...+Xn. (i) Calculate the moment generating function of X1. (ii) Hence find the moment generating function of Y. (iii) Hence calculate the expectation and variance of Y. (iv) Write down the name of the distribution of Y.

(b) Let X1,..., X, be independent Ber(0) random variables and let Y = X1 +...+Xn. (i) Calculate the moment generating function of X1. (ii) Hence find the moment generating function of Y. (iii) Hence calculate the expectation and variance of Y. (iv) Write down the name of the distribution of Y.

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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Question

Part B Urgently

1. (a) Let X be a continuous random variable with pdf
Sc(1 – x)? – b 0 <¤< 2
fx(x) =
otherwise,
for constants c>0 and b.
(i) Show that b cannot be positive.
(ii) Show that c =
(1+ 26).
Let b = -:
(iii) Find Fx(1), where Fx is the cdf of X.
(iv) Find P(X = 0).
(v) Find E[X].
(b) Let X1,..., Xn be independent Ber(0) random variables and let
Y = X1 +
...+ Xn.
(i) Calculate the moment generating function of X1.
(ii) Hence find the moment generating function of Y.
(iii) Hence calculate the expectation and variance of Y.
(iv) Write down the name of the distribution of Y.
(c) A car manufacturer claims that the fuel efficiency of its vehicles
meets a regulatory standard of 47 miles per gallon (mpg). To
assess this claim, the fuel efficiencies of a simple random sample
of 15 cars were measured. The mean of the 15 measurements was
= 46.75 mpg and their standard deviation was s 0.72 mpg.
y =
Assume that the measurements follow a Normal distribution.
(i) Conduct a test of size 5% of the null hypothesis that the
population mean efficiency is 47 mpg against the alternative
hypothesis that the population mean efficiency is less than 47
mpg. State clearly your test statistic, its null distribution, the
critical region, and your conclusion about the manufacturer's
claim.
(ii) Compute an equal-tailed 95% confidence interval for the
population mean efficiency.

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