23. A small press publishes an unpredictable number X of new books each month with(4+69)(3+7q))probability generating function πx(q) = E(q) =100a) Each book they publish in a given month has an 80% chance of reaching a best-seller list.What is the probability that next month all the books they publish will reach the best-seller list?(Hint: remember the post-test interpretation of π?)b) Calculate the expected value and variance of the number of books they will publish nextmonth.

The probability-generating function isprobability of chance reaching a best-seller list is 80%

Answered: 23. A small press publishes an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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f the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0.7, what is the probability that out of 8 newly hired people (A) 5 will still be with the company after 1 year? (B) 5 or more will still be with the company after 1 year? Round each of the calculations to three decimal places when going through the solution process.
Suppose 50% of the registered voters in a country are Republican if a sample of 598 voters is selected what is the probability that the simple proportion of republicans will be greater than 47% round your answer to 4 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.
please answer only page 167 3.1.30
Q3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.
which expressions correctly describes the experimental probability, P(B), where n(B) is the number of times event B occurred and n(T) is the total number of trials, T, in the experiment? a) P(B) = n(B) x n(T) b) P(B) = n(N) + n(T) c) P(B) = n(T)/n(B) d) P(B) = n(B)/n(T)
77. A system consists of five identical components connected in series as shown: 1 3 4 5 As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with 2 = .01 and that components fail independently of one another. Define events A; : at least t hours }, i = 1, ... , 5, so that the A;'s are independent events. Let X = the time at which the system fails- that is, the shortest (minimum) lifetime among the five components. a. The event {X > t} is equivalent to what event involving A1, ..., As? b. Using the independence of the five A;'s, com- pute P(X > t). Then obtain F(t) = P(X < 1) and the pdf of X. What type of distribution {ith component lasts does X have? c. Suppose there are n components, each having exponential lifetime with parameter å. What type of distribution does X have?
The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?

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