During my office hours (from 12pm to 6 pm), an average of about 1 student per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help?What is the mean number of students that will come see me on a particular day? Variance? Standard deviation? **Question 2:**During my office hours (from 12 PM to 6 PM), an average of about 1 student per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help? What is the mean number of students that will come see me on a particular day? Variance? Standard deviation?

Solution: Let X represents the number of student per hour comes in office for help . The random variable X has Poisson distribution with mean λ=1. X~Poisson(λ=1) P(X=x)=e-λλxx!; x=0,1, 2, .. The average or mean number of students per day comes in office for help is λ=1×6= 6 To find the probability that 6 students comes in for help that is to find P(X=6) P(X=6)=e-6×666!P(X=6)=0.002479×46656720P(X=6)= 115.660224720=0.160639P(X=6)= 0.1606 The probability that 6 students comes in for help is 0.1606 To find the the odds that on a particular day 6 students come in for help. Odds =Probability1-Probability Odds = 0.16061-0.1606Odds = 0.16060.8394=0.1913 to 1 The mean number of students in perticular day is Mean =λ=6 The variance is σ2=λ=6 The standard deviation is σ=λσ=6σ= 2.4495

Answered: During my office hours (from 12pm to 6…

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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During my office hours (from 12pm to 6 pm), an average of about 1 student per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help? What is the mean number of students that will come see me on a particular day? Variance? Standard deviation?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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