Example 5.5. The diameter of an electric cable, say X, is assumed to be a continuousrandom variable with p.d.f. :(i) Check that f(x) is p.d.f., andfx) %3 6х (1 — х), 0 b).

Answered: Image /qna-images/answer/76c63909-352d-4f29-b1d6-2a372de0138b.jpg

Answered: Example 5-5. The diameter of an…

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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Let X be a random variable. Which of the following statement is INCORRECT? If V (X) = 0, then there exists an x, such that Pr(X = x) = 1. There are cases that V(X) does not exist. By the definition of the random variable, the range of X is a subset of R; therefore, there must exist at least one x such that Pr(X = x) > 0. If Pr(X = 1) (E(X))².
Q1 Let X1 and X2 be independent exponential random variables with identical parameter A. Q1(i.) Find the distribution of Z = max(X1, X2). Q1 (ii.) Find the distribution of Y = min(X1, X2). Q1(iii.) Calculate E[Y]. Q1(iv.) Calculate E[Z]. Q1(v.) Using the relation Z = X1+X2 – Y, Calculate E[Z] and verify that it agrees with the calculation done in part (iv.)
The cumulative distribution function F(x) of a random variable X is given in the following table: 1 2 3 F(x) 0.5 b 1 a Let a and b are positive constants. If P(1 3) = 0.3. Then a and b equal to: a=0.1, b=0.3 None of these a=0.1, b=0.7 a=0.5, b=0.8
Prove the theorem
A3 Let X₁,..., Xn be independent and identically distributed random variables with E(X₂) μ and Var(X₂) = o². Let X = 1 X₁/n. Which of the following statements are true? (i) E(X) = μ/(n-1) (ii) E(X) = μ (iii) X is an unbiased estimator for μ (iv) E(X) = μ/n A: (i), (ii), and (iii) Circle the correct letter: B: (i) and (iii) C: (ii), (iii), and (iv) D: (ii) and (iii) E: (ii) and (iv) A B = CDE
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Example 5-5. The diameter of an electric cable, say X, is assumed to be a continuous random variable with p.d.f. : (i) Check that f(x) is p.d.f., and f(x) = 6x (1 – x), 0 b).