**5.80 Show that these facts are true.**Use the definition of binomial coefficients to show that each of the following facts is true. Then restate each fact in words in terms of the number of ways that \(k\) successes can be distributed among \(n\) observations.(a) \(\binom{n}{n} = 1\) for any whole number \(n \geq 1\). (b) \( \binom{n}{n-1} = n \) for any whole number \( n \geq 1 \).(c) \( \binom{n}{k} = \binom{n}{n-k} \) for any \( n \) and \( k \) with \( k \leq n \).

We expand left hand side i.e. nCn nCn= n!/n!*(n-n)! We know that 0!= 1 so nCn = n!/n! = 1 This…

Answered: 5.80 Show that these facts are true.…

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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Suppose that extensive testing has revealed that people in Group A have IQ’s that are well described by a N(100, 10) distribution while the IQ’s of people in Group B have a N(105, 10) distribution. What is the probability that a randomly chosen individual from Group A has a higher IQ than a randomly chosen individual fromGroup B?(a) Write a formula to answer the question. You don’t need to evaluate the formula.(b) Write some R code to answer the question.
In a certain industry, roughly 40% of managers have an advanced degree (Master's or beyond). From a group of 10 managers, X represents the number of them who have an advanced degree. What model is most appropriate for X? A. Poisson B. Binomial C. Binomial with n=10 and p=0.40 D. Poisson with λ=4λ=4
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Suppose that 3 out of every 5 drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. 15 drivers coming to an intersection under these conditions will be randomly selected. Let Y be the count of these selected drivers that come to a complete stop. Y has a binomial distribution where n = ___ and p = ___ . The possible values of Y are whole numbers from ___ to ___ .
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In a certain industry, roughly 40% of managers have an advanced degree (Master's or beyond). From a group of 10 managers, X represents the number of them who have an advanced degree. What model is most appropriate for X? A. Poisson B. Binomial C. Binomial with n=10 and p=0.40 D.Poisson with λ = 4

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5.80 Show that these facts are true. Use the definition of binomial coefficients to show that each of the following facts is true. Then restate each fact in words in terms of the number of ways that k successes be distributed among n observations. can (1) = 1 for any whole number n ≥ 1. (a)