Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min2.(a) What are the values of α and β?α = β = (b) What is the probability that a student uses the terminal for at most 21 min? (Round your answer to three decimal places.)(c) What is the probability that a student spends between 12 and 27 min using the terminal? (Round your answer to three decimal places.)

a) Given data Mean = 12 Variance = 36 Mean of gamma Distribution is given by E(X) = αβ = 12 Variance…

Answered: Suppose the time spent by a randomly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min².

(a) What are the values of α and β?

α =
β =

(b) What is the probability that a student uses the terminal for at most 21 min? (Round your answer to three decimal places.)

(c) What is the probability that a student spends between 12 and 27 min using the terminal? (Round your answer to three decimal places.)

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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