Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponentialn!distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula ():=k!(n - k)!(a) What is the probability that all thirteen bulbs fail before time t?(b) What is the probability that exactly k of the thirteen bulbs fail before time t?(c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that isexponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs failbefore time t?

From the given information, there are 13 lightbulbs. The lifetime of each is independent of each…

Answered: Suppose that you have thirteen…

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 company has seven applicants for two positions: three women and four men. Suppose that the seven applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of x. CAC. 3 X 2- X c²2 p(x): = p(x) = p(x): = p(x): = 4 X 2 - X mean = c³c. CAC 3 C² C p(x): = variance = X 2- X c²72 4 X 2 - x C³ C. X 4 2- X c²72 for x = 0, 1, 2 for x = = 0, 1, 2, 3, 4, 5, 6, 7 for x = 0, 1, 2, 3, 4, 5, 6, 7 for x = = 0, 1, 2 for x = (b) What are the mean and variance of this distribution? (Round your mean to one decimal place and your variance to two decimal places.) = 0, 1, 2
A poll of 220 students at a university reveals that 80 are taking a lab science course, and 55 are members of the Honors College, while 18 are taking a lab science and are members of the Honors College. Let L = the event that a student is taking a lab science, and H= the event that a student is a member of the Honors College. Complete parts (a) through (e) bel d. A student is randomly chosen. Find P(LH) and P((LH)) and explain what each number represents. P(LnH) (Simplify your answer.) = P((LnH)) = (Simplify your answer.) Explain what P(L n H) and P ((LH)) represent. Choose the correct answer below. O A. P(LnH) is the probability a student is taking a lab science and is a member of the Honors College. P ((LH)') is the probability a student is not taking a lab science or is not a member of the Honors College. O B. P(LnH) is the probability a student is taking a lab science or is a member of the Honors College. P ((LH)') is the probability a student is not taking a lab science or is not…
Chapters: Normal and Exponential random variables. Q: There exist naturally occurring random variables that are neither discrete nor continuous. Suppose a group of people is waiting for one more person to arrive before starting a meeting. Suppose that the arrival time of the person is exponential with mean 4 minutes, and that the meeting will start either when the person arrives or after 5 minutes, whichever comes first. Let X denote the length of time the group waits before starting the meeting. - a. Find P(0
1. Suppose you are a technician, whose repair time on a given job is said to follow an exponential distribution with expected time θ = 3 hours. You have 5 independent jobs lined up (you complete them sequentially, one by one). a. What is the probability of taking exactly 2 hours to finish a given job? b. What is the probability it will take more than 2 hours on a given job? c. You are on a given job and you already have been working for 1 hour. What is the probability it will at least an additional 2 hours to complete this job?
Find p(x) for x=0,1, 2, 3, 4, 5.
3. [From Meyer 1970] The following (somewhat simple-minded) weather forecasting is used by an amateur forecaster. Each day is classified as "wet" or "dry" and the probability that any given day is the same as the preceding one is assumed to be a constant p (0 < p < 1). Based on past records, it is supposed that January 1 has a probability of B of being "dry." Letting Br=probability (that the nth day of the year is "dry"), obtain an expression for Bn in terms of B and p. Also evaluate lim Bn and interpret your results.
T1.4 Suppose that 30% of all people who buy a new Iphone also buy an Apple watch. Consider randomly selecting 20 people who bought a new Iphone, and let X be the number of those who also bought an Apple watch. a) Find the probability that at least 6 of them bought an Apple watch. b) Find the probability that between 4 and 10 of them, inclusive, bought an Apple watch.
Find the probability P(Ec) if P(E)=0.17.
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
Q.3. Compute the probability that: (a) their sum is odd; (b) their product is even. Three distinct integers are chosen at random from the first 15 positive integers.
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