Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
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.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
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.
6. (Sec. 5.1) Two headlights of a car have the following joint pdf for their useful lifetimes X (the left
headlight) and Y (the right headlight)
ze(y+1) for r> 0.y > 0
f(x, y)
0 otherwise
(a) What is the probability that the lifetime X of the left headlight exceeds 2.8?
(b) Find the marginal pdfs of X and Y. Are the two lifetimes independent? Justify your answer
(c) What is the probability that the lifetime of at least one headlight does not exceed 2.8?
Thank you
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...
Knowledge Booster
Similar questions
- Q6. (a) Let X; (i = 1, ..,n) be independent random varables E(X;) = µ and var(X;) = of (i = 1, .,n). Let a = E-1 a; X; be an unbiased estimator of u where a; are constants. Find out how the a, are to be chosen if you wish to minimize var(@). (b) The bias and the mean squared error of an estimator Ô of a parameter 6 are defined as Bias (Ô) = b(ê ) = E(@) – 0 and m.s.e (@) = E{(@ – 0)?}, respectively. Show that m.s.e (@) var@) +{b(@ )}°.arrow_forwarda) 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.arrow_forwardThe random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationarrow_forward
- Let X1,..., Xn be iid pdf JKa,cx-a-1, f (x) = 0, x > c, x < c. and unknown parameters a and c. (a) Determine Ka.c. (b) Find the maximum likelihood estimator of c. (c) Find the maximum likelihood estimator of a. If you decide to use calculus methods, you have to do a second derivative test.arrow_forwardThe joint PDF of X and Y is given as f(x, y) = (2, 0Sxsys1 otherwise 0 a. Find the marginal PDF for X, f(x) and Y, f(y) b. Find &(Y) = a'Y + b", the Linear Mean Square Error (LMSE) estimator of X given Y c. Find ei, the minimum Mean Square Error (MSE) of the optimum linear estimatearrow_forward4. Let X and Y have the joint pmf defined by f(0,0) = f(2,1) = 0.3, f(1,0) = f(1,1) = 0.2(a) Depict the points and corresponding probabilities on a graph.(b) Give the marginal pmfs in the “margins.”(c) Compute μX, μY, σ2X, σ2Y, Covariance(X,Y ), and ρ.(d) Find the equation of the least squares regression line and draw it on your graph. Doesthe line make sense to you intuitively?arrow_forward
- 9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdf f(x, y) = 8xy, %3D (a) [10 points] Find fa(1) and fy(y). (b) [15 points] Find Cov(X,Y) and correlation coefficient.arrow_forwardFind the marginal PDFs of X and Y.arrow_forwardb) A random variable X follows an exponential distribution, X~Exp(0), with parameter 0 > 0. Find the cumulative distribution function (CDF) of X. i) ii) Show that the moment generating function (MGF) of X is M(t) = iii) Use the MGF in (ii) to find the mean and variance of X.arrow_forward
- Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by Sk(6–x), 0arrow_forwardLet x and y be joint continuous random variable with joint pdf f XY (x, y) = { cx+ 1, x, y≥ 0, x+y< 1 0, otherwise 1. Find the constant c. 2. Find the marginal PDF’S fX (x) and fY (y) 3. Find P(Y<2X^2 )arrow_forwardAssume that X and Y are independent random variables where X has a pdf given by fx(x) = 2aI(0,1)(x) and Y has a pdf given by fy(y) = 2(1– y)I(0,1)(y). Find the distribution of X + Y.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage