**Exercise 2.**Consider the process \( Y: RE_1 \), where \( Y = \) "total number of up-dots on 4 dice" and \( RE_1 = \) "roll 4 dice."Note that \( Y: RE_1 \sim X_1 + X_2 + X_3 + X_4 \), where the \( X_i \)'s are IID with common PMF\[P(X_1 = j) = \frac{1}{6} \, (j = 1, \ldots, 6).\]Here, \( X_i \) measures the number of up-dots on the \( i^{th} \) rolled die, \( i = 1, 2, 3, 4 \).(a) Compute \( \text{mean}(Y:RE_1) \). Hint: \( E(Y) = E(X_1 + X_2 + X_3 + X_4) \).(b) Compute \( \text{var}(Y:RE_1) \). Hint: \( \text{var}(Y) = \text{var}(X_1 + X_2 + X_3 + X_4) \).I generated data \( Y:S \), where sample \( S \) is an outcome of \( RE_1 (N \equiv 10^6) \).(c) Explain why you would expect the sample distribution \( \text{dist}(Y: S) \) to be approximately equal to the process distribution \( \text{dist}(Y: RE_1) \). That is, what fundamental result leads to this expectation and why is it applicable?(d) I computed the sample mean of my data, \( \text{mean}(Y: S) \). What value [approximately] do you think it was? Explain why your approximate value is likely very reasonable.(e) I computed the sample variance of my data, \( \text{var}(Y: S) \). What value [approximately] do you think it was? Explain why your approximate value is likely very reasonable.(f) I computed the sample proportion of my data values equal to 4, \( \text{prop}_S(Y = 4) \). What value [approximately] do you think it was? Explain why your approximate value is likely very reasonable.

Given that - P( Xi = j ) = 1/6. j = 1, 2, 3, 4, 5, 6. i =…

Answered: Consider the process Y: RE,, where 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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