1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density functionf(x)= 20-x-(3-x)³ for 0≤x≤ 3 and 0 otherwise.243d) What is the expected value of X (E(X))?e) What is the expected value of X-3? [f) What is the expected value of 6X?Please solution USING R script

A random variable X has following probability density function: fx=20243 x3-x3 ; 0≤x≤3 By…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density functionf(x)= 20·x·(3−x)^3/243 for 0 ≤ x ≤ 3 and 0 otherwise. e) What is the expected value of X - 3? f) What is the expected value of 6X? g) What is the expected value of X2? h) What is the probability that X is greater than its expected value? i) What is the expected value of X3−3X+1? j) What is the 55th percentile of X? k) What is the probability that X is within 0.4 of its expected value? l) What is the probability that X = 2?
Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
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1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density function f(x)= 20-x-(3-x)³ for 0 ≤ x ≤ 3 and 0 otherwise. 243 d) What is the expected value of X (E(X))? e) What is the expected value of X-3? | f) What is the expected value of 6X?