Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Question
Chapter 4.2, Problem 2E
(a)
To determine
To Show: The points and corresponding probabilities on a graph.
(b)
To determine
To find: The marginal pmfs.
(c)
To determine
To find: The values of
(d)
To determine
To find: The equation of regression line and plot it on graph. Also, to check if it makes sense or not.
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Students have asked these similar questions
a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results.
Calculate E[X2].
(b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.
Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure.
3₂
(0, 1)
(-1,0)
(a) Find Cov(Y₁ Y₂).
Cov(Y₁, Y₂)
=
(b) Are Y₁ and Y₂ independent?
Yes
O No
(1, 0)
(c) Find the coefficient of correlation for Y₁ and Y₂.
P=
y/₁
(d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not?
O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent.
Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent.
O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent.
O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
Suppose X, Y joint Gaussian with s.d.'s 2 and 3 respectively and
covariance 4. Find the joint pdf and the two marginal pdf's. What if
the covariance were 8?
Chapter 4 Solutions
Probability and Statistical Inference (9th 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 - A particle starts at (0,0) and moves in one-unit...Ch. 4.1 - In a smoking survey among boys between the ages of...Ch. 4.1 - A manufactured item is classified as good, a...Ch. 4.2 - Prob. 1E
Ch. 4.2 - Prob. 2ECh. 4.2 - Roll a fair four-sided die twice. Let X equal the...Ch. 4.2 - Let X and Y have a trinomial distribution with...Ch. 4.2 - Prob. 5ECh. 4.2 - The joint pmf of X and Y is f(x,y)=16,0x+y2, where...Ch. 4.2 - Let the joint pmf of X and Y be...Ch. 4.2 - A certain raw material is classified as to...Ch. 4.2 - Prob. 9ECh. 4.2 - If the correlation coefficient exists, show that...Ch. 4.3 - Let X and Y have the joint pmf...Ch. 4.3 - Let the joint pmf f(x,y) of X and Y be given by...Ch. 4.3 - Let W equal the weight of laundry soap in a...Ch. 4.3 - The gene for eye color in a certain male fruit fly...Ch. 4.3 - Let X and Y have a trinomial distribution with...Ch. 4.3 - An insurance company sells both homeowners...Ch. 4.3 - Using the joint pmf from Exercise 4.2-3, find the...Ch. 4.3 - A fair six-sided die is rolled 30 independent...Ch. 4.3 - Let X and Y have a uniform distribution on the set...Ch. 4.3 - Let fX(x)=110,x=0,1,2,...,9, and...Ch. 4.3 - Suppose that X has a geometric distribution with...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Show that the expression in the exponent of...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal...Ch. 4.5 - Let X denote the height in centimeters and Y the...Ch. 4.5 - For a freshman taking introductory statistics and...Ch. 4.5 - For a pair of gallinules, let X equal the weight...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal distribution....Ch. 4.5 - In a college health fitness program, let X denote...Ch. 4.5 - For a female freshman in a health fitness program,...Ch. 4.5 - Prob. 12ECh. 4.5 - An obstetrician does ultrasound examinations on...
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