Problem 4. A machine receives signals, and the number of signals it receives has a Poisson (X)distribution. The signal is either positive or negative, and the probability for the signal tobe positive is p. Signals are mutually independent, and are independent of the number ofsignals the machine receives. Let the number of positive signals it receives be n₂ and findthe distribution of η.

Given: The number of signals the machine receives has a Poisson distribution. The signal is either…

Answered: Problem 4. A machine receives signals,…

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.) In an experiment on the behavior of young children, each subject is placed in an area with 5 toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows. Number of Toys Probability 2 3 4 5 0.03 0.16 0.30 0.23 0.17 a.) Find the P(X = 5). b.) If a subject is chosen at random, what is the probability they played with more than 2 toys? c.) If a subject is chosen at random, what is the probability they played with less than 3 toys? d.) Find the expected number of toys played with. e.) Find the standard deviation of the number of toys played with.
8.
8. The probability distribution of weekly sales of TV sets in a retail depot is given berow : 12 13 14 15 Demand (units) 10 11 0-05 0-10 0.25 0-40 0-15 0-05 Probability The depot earIS a profit of should be stocked ? 700 per set. If it is not sold, the loss is 300 per set. How many sets
Example 2.3.8 Six dissimilar (distinguishable) balls are distributed at ran- dom into 3 boxes. Find the probability that these boxes contain 3, 2 and 1 balls respectively.
13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(205
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
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.
Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
Consider an M/M/1 queuing system with mean inter arrival time of 4 minutes. The average service time for each customer is 3 minutes. The probability that there are 3 arrivals in the system is closest to O a. None of these O b. 0.105 Oc. 0.895 O d. 0.422
5. pg 359 Baby elk and their chances Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X = the number who survive to adulthood. The probability distribution of X is shown here. Find the probability that fewer than 3 of the elk survive to adulthood. 0 1 2 3 4 5 6 7 Probability 0.0173 0.0950 0.2239 0.2932 0.2304 0.1086 0.0284 0.0032 Value
1. The following table shows the probabilities associated with the discrete random variable, which counts the number of sales performed at a peak hour in a store in a downtown commercial. It is known that the probability that at most three sales is 40%, that at least five sales are made is 55%, but having less than 6 sales is 63%. one). Find the values of a, b, and c. two). Calculate the cumulative distribution function 3). Find the expectation and variance
5. Based on recent records, the manager of a car painting centre has determined the following probability distribution for the number of customers per day: 1 3 4 P(X = x) 0.05 0.2 0.3 0.25 0.15 0.05 А. f the centre has the capacity to serve three customers per day, what is the probability that one or more customers will be turned away on a given day? В. What is the probability that the centre's capacity will not be fully utilized on a day? С. away is no more than 0.1? By how much the capacity must be increased so the probability of turning customer 2. il

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