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A First Course in Probability (10th Edition)

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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**Problem 6.6:**

A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by \(N_1\) the number of tests made until the first defective is identified and by \(N_2\) the number of additional tests until the second defective is identified. Find the joint probability mass function of \(N_1\) and \(N_2\).

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A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 8 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured and pays a fixed sum on death. All 8 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. Part a) What is the expected number of policies that will pay out before the insured parties have reached age 61? Part b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? Part c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?
Suppose that three balls are randomly chosen without replacement from a box containing 4 white and 7 black balls. Let Xi be 1 if i th ball selected is white, ant let it be 0 otherwise.a. Write down Probability mass functions of X1, X2 and X3 in tabular form;b. Write down the joint probability mass function of X1, X2;c. Find the joint probability mass function of X1, X2 and X3. Repeat this problem, when the ball is replaced in the box before the next selection. Please justify your answers. Thanks!
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The following table gives the total endothermic reactions involving sodium bicarbonate Final Temperature Conditions Number of Reactions 266 K 271 K 60 274 K 92 Assume that reactions are independent. What is the probability that the 2nd reaction to result in a final temperature less than 272K occurs within three or fewer reactions? Report answer 3 decimal places.
3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by N1 the number of tests made until the first defective is identified and by N2 the number of additional tests until the second defective is identified. Find the joint probability mass func- tion of N1 and N2.
4.6. Consider the following history of six events in which operations span multiple ob- jects, assuming that A and B are initialized to 0: ev = inv(write(1)) on evz = inv(sum() evy = resp(urite()) from A evA = inv(write(2)) on evs = resp(write()) from B evg = resp(sum(2)) from A, B at P at P А, В at Pa at P at P at Ps A on B Show that this history is not linearizable but normal.
please answer only page 167 3.1.30
The time that it takes to service a car is an exponential random variable with rate 1.1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability thatB’s car is ready before A’s? Assume that the service times are independent, and the servicebegins upon arrival.2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has beencompletely serviced, what is the probability that B’s car is ready before 2? Detailed explanation and calculation would be much appreciated.
4. A die is rolled twice. Determine the probability that a 5 is rolled on the first roll and any number other than 5 is rolled on the second ra a. O Pr(5n5') b. O Pr(5n5') co Pr(5n5')= d. O Pr(5n5') = 35 Aspley SHS 14 March 2019
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