Consider a multinomial experiment. This means the following. 1. The trials are independent and repeated under identical conditions. 2. The outcomes of each trial falls into exactly one of k 2 2 categories. 3. The probability that the outcomes of a single trial will fall into the îth category is p, (where i = 1, 2..., k) and remains the same for each trial. Furthermore, p, + P, + ... + Pp = 1. 4. Let r, be a random variable that represents the number of trials in which the outcomes falls into category i. If you have n trials, then r, +r, +... +r, = n. The multinomial probability distribution is then the following. n! How are the multinomial distribution and the binomial distribution related? For the special case k = we use the notation r, =r, r, = n -r, P, = p, and p, - g. In this special case, the multinomial distribution becomes the binomial distribution. A city is having an election to determine the establishment of a new municipal electrical power plant. The new plant would emphasize renewable energy (e.g., wind, solar, geothermal). A recent large survey of voters showed 70% favor the new plant, 20% oppose it, and 10% are undecided. Let p, = 0.7, p, = 0.2, and p, = 0.1. Suppose a random sample of n = 8 voters is taken. (a) What is the probability that r, = 4 favor, r, = 3 oppose, andr, = 1 are undecided regarding the new power plant? (Round your answer to three decimal places.) (b) What is the probability that r, = 5 favor, r, = 3 oppose, andr, = 0 are undecided regarding the new power plant? (Round your answer to three decimal places.)

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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Consider a multinomial experiment. This means the following. (refer to screenshot)

A city is having an election to determine the establishment of a new municipal electrical power plant. The new plant would emphasize renewable energy (e.g., wind, solar, geothermal). A recent large survey of voters showed 70% favor the new plant, 20% oppose it, and 10% are undecided.

Consider a multinomial experiment. This means the following.
1. The trials are independent and repeated under identical conditions.
2. The outcomes of each trial falls into exactly one of k > 2 categories.
3. The probability that the outcomes of a single trial will fall into the ith category is p; (where i = 1, 2. .., k) and remains the same for each trial. Furthermore, p, + p, + ... + Pk = 1.
4. Let r; be a random variable that represents the number of trials in which the outcomes falls into category i. If you have n trials, then r, +r, +... + r, = n. The multinomial probability distribution is then the
following.
n!
r!r,! ....
How are the multinomial distribution and the binomial distribution related? For the special case k = 2, we use the notation r, = r, r, = n – r, p, = P, and p, = q. In this special case, the multinomial distribution
becomes the binomial distribution.
A city is having an election to determine the establishment of a new municipal electrical power plant. The new plant would emphasize renewable energy (e.g., wind, solar, geothermal). A recent large survey of voters
showed 70% favor the new plant, 20% oppose it, and 10% are undecided. Let p, = 0.7, p, = 0.2, and p3 = 0.1. Suppose a random sample of n = 8 voters is taken.
(a) What is the probability that r, = 4 favor, r, = 3 oppose, and r, = 1 are undecided regarding the new power plant? (Round your answer to three decimal places.)
(b) What is the probability that r, = 5 favor, r, = 3 oppose, and r, = 0 are undecided regarding the new power plant? (Round your answer to three decimal places.)

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