Question 4: Exponential random variables (sometimes) give good models for the time to failure ofmechanical devices. For example, we might measure the number of miles traveled by a given car beforeits transmission ceases to function. Suppose that this distribution is governed by the exponentialdistribution with mean 100,000. What is the probability that a car's transmission will fail during its first50,000 miles of operation?

Answered: Question 4: Exponential random…

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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QUESTION 8 You may need to use the appropriate appendix table or technology to answer this question. A population proportion is 0.50. A sample of size 100 will be taken and the sample proportion p will be used to estimate the population proportion. (Round your answers to four decimal places.) (a) What is the probability that the sample proportion will be within ±0.03 of the population proportion? (b) What is the probability that the sample proportion will be within ±0.05 of the population proportion?
QUESTION 12 A random variable X has the following distribution: X -1 0 1 P(X=x) 3 .5 .2 Let Y=X². Find the expected value of random variable Y. .38 .6 0.5 4
QUESTION 12 A random variable X has the following distribution: X -1 0 1 P(X=x) 3 .5 .2 Let Y=X². Find the expected value of random variable Y. .38 .6 0.5 4
Question 13 The following table lists the number of homework problems X that appear on a Probability and Statistics exam, and the corresponding probability. Note X is a random variable. Find the moment generating function of X. P(X) 14 .1 15 .2 16 .3 17 .4 Note exp(z) = e^z (the exponential function). O .1xexp(14t) + .2xexp(15t) + .3xexp(16t) + .4xexp(17t) .1хеxp(14t) 4xеxp(17t) O 1
QUESTION 1 The same scenario is used for all questions. New parents in a little town buy two major brands of infant formulas, labeled A and B. After some intensive study, a marketing researcher for one of the manufacturers found that the probability of parents purchasing A or B is based on the parents' most recent purchase. Suppose that the following transition probabilities are appropriate O Probabilities of Parents Purchasing A or B From A To A To B O A B B Which of the following is the correct two period tree diagram for a customer who last purchased Brand A? O A 0.75 A 0.20 0.25 0.75 0.75 0.25 0.25 0.75 A B A B A 0.25 B 0.80 0.75 0.25 0.20 0.80 0.75 0.25 0.20 0.80 0.25 0.75 0.20 0.80 A B A B A B A B A B A B (0.25)(0.75)-0.1875 (0.25)(0.25) 0.0625 (0.75)(0.20) 0.1500 (0.75)(0.80)-0.6000 (0.75)(0.75)=0.5625 (0.75)(0.25)-0.1875 (0.25)(0.20)-0.0500 (0.25)(0.80)-0.2000 (0.25)(0.25) 0.0625 (0.25)(0.75)-0.1875 (0.75)(0.20) 0.1500 (0.75)(0.80) 0.6000
Question 4 Suppose that in a population of twins, males (M) and females (F) are equally likely to occur and that the probability that twins are identical is 0. If twins are not identical, their genders are independent (if they are identical, their genders are the same). (i) Show that, ignoring birth order, P(MM) = P(FF) = (1+0)/4 and P(MF) = (1–0)/2. (ii) Suppose that n twins are sampled. It is found that n₁ are MM, n2 are FF, and në are MF, but it is not known which twins are identical. Find the maximum likelihood estimator of 0.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
Question 3, section 6.1

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