The amount of the product of a controlled laboratory experiment, has the following cumulative distribution function F:F(x) = 0 for x < 0 and F(x)=³ for 0 ≤ x ≤ 3 and F(x) = 1 for x > 327a) What is the probability density function for X for 0 ≤ x ≤ 3?○ f(x) =f(x) =160f(x) == //f(x)(=/3/7/26* ~*f(x) == /b) What is the probability that X > 1.2? 2c) What is the probability X < 1.2? 34d) What is the probability that X < 0 ?e) What is the probability that X > 2.2 ?5f) What is the probability that X > 2.2 given that X > 1.2?6g) Calculate the median of X. 7h) What is the expected value of X?8i) What is the expected value of x²?j) What is the variance of X?k) What is the probability that X is more than 0.2 above its expected value?1011

As per our guidelines we are suppose to answer only three sub parts. Given,F(X)={x327; 0≤x≤30;…

Answered: The amount of the product of a…

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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Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…

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