Probability And Statistical Inference (10th Edition)

10th Edition

ISBN: 9780135189399

Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Publisher: PEARSON

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Textbook Question

Chapter 4.1, Problem 3E

Let the joint pmf of X and Y be defined by f ( x , y ) = x + y 32 , x = 1 , 2 , y = 1 , 2 , 3 , 4.

(a) Find f X ( x ) , the marginal pmf of X.

(b) Find f Y ( x ) , the marginal pmf of Y.

(d) Find P ( Y = 2 X ) .

(f) Find P ( X ≤ 3 − Y ) .

(g) Are X and Y independent or dependent? Why or why not?

(h) Find the means and the variances of X and Y.

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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Chapter 4.1, Problem 2E

Chapter 4.1, Problem 4E

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Chapter 4 Solutions

Probability And Statistical Inference (10th Edition)

Ch. 4.1 - For each of the following functions, determine the...Ch. 4.1 - Roll a pair of four-sided dice, one red and one...Ch. 4.1 - Let the joint pmf of X and Y be defined by...Ch. 4.1 - Select an (even) integer randomly from the set...Ch. 4.1 - Each part of Figure 4.1-5 depicts the sample space...Ch. 4.1 - The torque required to remove bolts in a steel...Ch. 4.1 - Roll a pair of four-sided dice, one red and one...Ch. 4.1 - Each part of Figure 4.1-6 depicts the sample space...Ch. 4.1 - A particle starts at (0,0) and moves in one-unit...Ch. 4.1 - In a smoking survey among boys between the ages of...

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