6.15) Consider a sequence of independent trials, with each trial beinga success with probability p. Given that the kth success occurs ontrial n, show that all possible outcomes of the first n 1 trials thatconsist of k 1 successes and n -k failures are equally likely.-

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Answered: 6.15) Consider a sequence of…

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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3. An unloaded, 4-sided dice is rolled twice. Let X be the maximum number obtained from the two rolls, and Y be the minimum number from the two rolls. (The dice can show the numbers 1, 2, 3, or 4, each with probability 1/4. As an example, if the two rolls are 1 followed by 3, then X = 3 and Y = 1.) (a) Find the joint pmf of X and Y. (b) Find the conditional pmf of X given that Y = 2. (Hint: part (a) is similar to a problem from Modelling Uncertainty. Please express your answers in table form, and please use fractions in lowest terms.)
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1 of 2 Based on a smartphone survey, assume that 55% of adults with smartphones use them in theaters. In a separate survey of 234 adults with smartphones, it is found that 127 use them in theaters. a. If the 55% rate is correct, find the probability of getting 127 or fewer smartphone owners who use them in theaters. b. Is the result of 127 significantly low? 0 of 2 ts a. If the 55% rate is correct, the probability of getting 127 or fewer smartphone owners who use them in theaters is (Round to four decimal places as needed.) b. Is the result of 127 significantly low? v than the probability cutoff that corresponds to a significant event, which iv 0.5. v because the probability of this event is 0.95. 0.05. 1 of 1 cents 1 of 1 cess 1 of oo Library otions 0 of 2 ? Enter your answer in the answer boOx. This course (Elementary Statistics Section T) is based on Triola: Elementary Statistics, 13e d山T。 1386 4. PAGES W NOV 22 3D MacBook Air DII DD 80 000 D00 F8 F9 F10 55 F6 F7
2. [7: 2,2,3] Mong Corporation makes auto batteries. The company claims that 80% of its LL70 batteries are good for 70 months or longer. Assume that this claim is true. Let ô be the proportion in a sample of 100 such batteries that are good for 70 months or longer. What is the probability that p is: a) Within .05 of the population proportion? b) Less than the population proportion by .06 or more? c) Greater than the population proportion by .07 or more?

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6.15) Consider a sequence of independent trials, with each trial being a success with probability p. Given that the kth success occurs on trial n, show that all possible outcomes of the first n 1 trials that consist of k 1 successes and n -k failures are equally likely. -