Consider the probability density function0if x < 0f(x) =32x4Find Var(X).Select one:OA WIN w/00−216if 0 ≤ x ≤ 1if x > 1.

Given,the probability density function of X isf(x)=0if x<012if 0≤x≤132x4if x>1

Answered: Consider the probability density…

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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A random variable X has probability density function for 0 < x < 2, 4 f(x) = { +(2x –- 3) for 2 < x < 3, otherwise. Calculate µ, the mean value of X. Give your answer to three decimal places.
Let X be the time in hours that the battery of a solar calculator functions properly between exposures to light sufficient to recharge it. Suppose the density of X is given by:f(x) = (50/6)x^-3 2 < x < 10.a) Verify that this is a valid continuous density. b) Calculate the expression for the cumulative distribution function of X and use it to calculate the probability that the charge of a randomly selected solar cell will last at most four hours before it needs to be used.at most four hours before it needs to be recharged. c) Calculate the average time that a battery charge lasts before it needs to be recharged. d) Calculate E[X2] and use its value to determine the variance of X.
6.The continuous random variable X has the probability density function given by 1 -2 < x < 4 f(x) = otherwise Determine P(X < 2)
Show that the standard normal probability density function f(x) has points of inflection when x = ±1.
The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

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Consider the probability density function 0 if x < 0 f(x) = { // 3 2x4 Find Var(X). if 0 ≤ x ≤ 1 if x > 1.