10. Let N be a fixed large integer. Consider n independent trials, each of which is a successwith probability 1/N. Recall that the gambler's rule (see Example 1.6.3) says that ifn 2 N, the chance of at least one success in n trials is about 1/2. Show that ifN, then the chance of at least two successes is about 1/2.

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Answered: 0. Let N be a fixed large integer.…

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 binary message (0 or 1) is communicated through a noisy channel with A as the message transmitted and B as the message received. Assume that A=0 and A=1 is transmitted with equal probability, and the received message is 90% correct of the time. With this, determine the joint PMF of A and B. Choose the answer for each question among the following: 0.05, 0.10, 0.40, 0.45. ii. 111. iv. P(A=1, B=0) P(A=1, B=1) P(A=0, B=1) P(A=0, B=0)
6.34. Jay has two jobs to do, one after the other. Each attempt at job i takes one hour and is successful with probability p¡. If p₁ = .3 and p2 = .4, what is the probability that it will take Jay more than 12 hours to be successful on both jobs?
Please answer d and e. P.9.2
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How can I solve that question 3.7 (a and b)?
4. A weighted die has a probability of a 6 being p where 0 < p < 1. Chris rolls the die 3 times. Let X be the number of times 6 appears on the die. Z is the number of times any number other than 6 appears on the last two tosses. Find the population covariance between X and Y. Interpret the meaning of the value in context of the problem.
2. Suppose you are at a birthday party with n other people. How large must n be to ensure that the probability that you share your birthday with at least one other person is greater than 1/2?
Consider the following game in a game arcade. The probability of winning a game is p and hence loosingthe game is 1 − p. In order to win a prize you are given three choices:• A: win at least once in 6 games;• B: win at least twice in 12 games; and• C: win at least 3 times in 18 games.1. If p = 16 which of A, B, or C should you choose to maximize your probability of winning the prize?You are required to compute the probabilities for each option to justify your answer.2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probabilityof winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 inincrements of 0.1. Summarize your observation.Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the threecurves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure toadd a legend that identifies the curves for the three different options…
Suppose the weather moves between three states 1,2,3. It stays in state 1 for an exponentially distributed number of days with mean 3, then goes to state 2. It stays in state 2 for an exponentially distributed number of days with mean 4, then goes to state 3. It stays in state 3 for an exponentially distributed number of days with mean 1, then goes to state 1. Compute the long-term probability that the weather is in state 1. Write your answer as a decimal.

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