Q1QIA Suppose that the probability of finding defectives within a manufactured lot of electricalfuses is 0.2. Assume the probability distribution is binomial. Let X be the number ofdefectives within the sample. In a sample of 16 fuses, find the probabilities (a) P(X=2),(b) PX22), (c) P(1 < X <3). (1)B Suppose the discrete random variable X has the probability distribution listed in the tablebelow. Find: (a) P(11 < X < 15), (b) E(4X-7).12131114f(x) 0.039 0.175 0.248 0.107150.1616170.125 0.146

1)A)Givensample size(n)=16p=0.2Let "x" be the no.of defectives within the…

Answered: QIA Suppose that the probability of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2) A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. What is the probability that the second pipe (with length Y) is more than 0.35 feet longer than the first pipe (with length X)? Give your answer to four decimal places. Hint: Do not use calculus to get your answer.
a. What is the probability that a jet engine will last less than 12 months before needing to berebuilt? b. What is the probability that a jet engine will last more than 12 months before needing to berebuilt? c. Given a jet engine has lasted more than 6 months, what is the probability it will last morethan 12 months before needing a rebuild?
TABLE 13.6 Let X and Y be two random variables each X -1 tuking three values -1, 0 and 1, and having the joint probability distribution as given in Table 13-6. Y Obiain the marginal probability distributions of X and Y and hence their expected values. •2 •2 -2 1-
2) The number x of people admitted to an intensive care unit in a particular hospital, on any given day, has a Poisson probability distribution with mean equal to five (5) people per day. What is the probability that the number of people admitted to an intensive care unit on a particular day is three (3)? Solve using Poisson's formula (Mendenhall et al., 2015).
Let the random variable X follows binomial distribution with parameters 14 and 5/12. Find P(X greater than 12).
Suppose that the joint probability for random variables X and Y defined by 29 28 3. 28 28 The mean of the random variable Y. HY.is 39 28 27 28 41 28
5. The probability distribution of the discrete random variable X is f(x) = x = 0,1, 2,3. Find the mean of X.
Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 6 and 10 minutes. Let X = the time, in minutes, it takes Lizzie to eat an apple. What is the probability that it takes Lizzie more than 11 minutes to finish the next apple? What is the probability that it takes Lizzie at least 7.2 minutes to finish the next apple? What is the probability that it takes Lizzie fewer than 6.3 minutes or more than 8 minutes to finish the next apple?
11
9
For the probability distribution of a discrete random variables, the probabilities of any single value of x is always
10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?

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