ONLY QUESTION 2 These questions are in most cases taken from Newbold et al. For numericalquestions, obtain an answer both with a computer program such as Matlab, R, orPython and with tables if you are able to do so, but solve with tables in any event.1. A random variable has the density function: fx(x) = 0, if x < 3; x − 3, if 3 ≤x ≤ 4; 5 – x, if 4 < x < 5; 0, x ≥ 5.Using the expression for the expectation (mean) of a continuous random vari-able, i.e.E(X) =xfx(x)dx,treating the two intervals 3 ≤ x ≤ 4 and 4 ≤ x ≤ 5 separately, show that the meanof this random variable is 4.2. (a) Using the expression for variance in either the discrete or continuous case,show that for a random variable X and fixed parameters a and b, var(a + bx) =b²var (X).(b) Using the expression K(X) = E(X−µ) as a kurtosis measure, show that fora random variable X and fixed parameters a and b, K(a + bX) = K(X). Interpretthis with respect to the standardization by ¹.3. Let X₁ and X₂ be a pair of random variables. Show that the covariance betweenthe random variables (X₁ + X₂) and (X₁ – X₂) is 0 if and only if X₁ and X₂ havethe same variance.

Given information: The statement is given related to the property of change of Origin and scale with…

2. (a) Using the expression for variance in either the discrete or continuous case, show that for a random variable X and fixed parameters a and b, var(a + bX) = b²var(X). = (b) Using the expression K(X) = E(X−µ)² as a kurtosis measure, show that for a random variable X and fixed parameters a and b, K(a+bX) = K(X). Interpret this with respect to the standardization by σ¹.

2. (a) Using the expression for variance in either the discrete or continuous case, show that for a random variable X and fixed parameters a and b, var(a + bX) = b²var(X). = (b) Using the expression K(X) = E(X−µ)² as a kurtosis measure, show that for a random variable X and fixed parameters a and b, K(a+bX) = K(X). Interpret this with respect to the standardization by σ¹.

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.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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