a Find the mean and the variance of pollutants per sample when the cleaning device is not in place.b Find the mean and the variance of pollutants per sample when the cleaning device is in place. abFind the mean and the variance of pollutants per sample when the cleaning device is not in place.Find the mean and the variance of pollutants per sample when the cleaning device is in place. 6.34 As in Exercises 6.6, 6.10, and 6.20, in a study of the particulate pollution in air samples overa smokestack, X represents the amount of pollutants per sample when a cleaning device is notoperating, and Y represents the amount per sample when the cleaning device is operating. Assumethat (X, Y) has a joint probability density functionf (x, y) =1,for 0 ≤ x ≤ 2;0 ≤ y ≤ 1; 2y ≤ xelsewhere.

Given that, the joint pdf of X and Y is, f(x,y)= 1 ; 0<=x<=2 ; 0<=y<=1 ; 2y<=x…

Answered: 6.34 As in Exercises 6.6, 6.10, and…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 2E

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a Find the mean and the variance of pollutants per sample when the cleaning device is not in place.
b Find the mean and the variance of pollutants per sample when the cleaning device is in place.

a
b
Find the mean and the variance of pollutants per sample when the cleaning device is not in place.
Find the mean and the variance of pollutants per sample when the cleaning device is in place.

6.34 As in Exercises 6.6, 6.10, and 6.20, in a study of the particulate pollution in air samples over
a smokestack, X represents the amount of pollutants per sample when a cleaning device is not
operating, and Y represents the amount per sample when the cleaning device is operating. Assume
that (X, Y) has a joint probability density function
f (x, y) =
1,
for 0 ≤ x ≤ 2;0 ≤ y ≤ 1; 2y ≤ x
elsewhere.

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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