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.243g) 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?Please solution USING R script

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

Answered: 1. The error, X, in measuring the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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?
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.a) What is the probability that X > 1? b) What is the probability that X < 1? c) What is the probability that 2.1 < X < 2.7? d) What is the expected value of X (E(X))?
From the density of the image below what is the probability that x is at least 0.34 ?
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Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)
On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
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