The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over aperiod of one year is a continuous random variable X that has the density function of0

Introduction: Denote the random variable X as the duration (100 hours) for which a family runs their…

Answered: The total number of hours, measured in…

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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The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function shown below. Find the probability that over a period of one year, a family runs their vacuum cleaner (a) less than 120 hours; (b) between 55 and 85 hours. f(x) = x, 0<x<1 2−x, 1≤x<2 0, elsewhere A.) The probability the family runs the vacuum cleaner less than 120 hours is B.) The probability the family runs the vacuum cleaner between 55 and 85 hours is
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. What is P(X ≤ 4)? What is P(4.5 < X)?
The joint density function of the random variables X and Y is given by f(x, y) = x + y for 0 ≤ x, y ≤ 1 and f(x, y) = 0 otherwise. Consider the circle centered at the origin and passing through the point (X, Y). What is the probability that the circumference of the circle is no more than 2π?
A continuous random variable has a density function f (X)=2(5-x)/5 , where 2<x<3. Calculate the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet: P (x < 2.5) P (x > 2.2) P (2.1 ≤ ? ≤ 2.7)
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A continous random variable X has the density function. f(x) = {x, 0 < x ≤ 1, {2 − x, 1 < x ≤ 2, {0, elsewhere. (a) Show that P(0 < X < 2) = 1 (b) Find P(X < 1.2)
A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculatethe following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet:P (x < 2.5)P (x > 2.2)P (2.1 ≤
The experiment is to toss two balls into four boxes in such a way that each ball is equally likelyto fall in any box. Let X denote the number of balls in the first box.a. What is the CDF of X?b. What is the density function of X?

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The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function of 0