Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
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Textbook Question
Chapter 4.4, Problem 6E
Using Example 4.4-2,
(a) Determine the variances of X and Y.
(b) Find
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Let X have a mean of 132 and a variance of 32. Define Y = X² + 2X + 1. Compute the (a) mean and (b) variance of Y.
(a) i
(b) i
1 The menu at a café is shown below.
Main coursе
Dessert
Fish and Chips
$3
Ice Cream
$1
Apple Pie
Sponge Pudding
Spaghetti
$3.50
$1.50
Pizza
$4
$2
Steak and Chips $5.50
The owner of the café says that all the main-course dishes sell equally well, as
do all the desserts, and that customers' choice of dessert is not influenced by
the main course they have just eaten.
The random variable X takes value O with probability, and value 1 with the remaining
probability.
The random variable Y takes value 100 with probability and value 101 with the remaining
probability.
What is the relation between the variance of X and the variance of Y?
Var[X] Var[Y]
"
Chapter 4 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
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...
Ch. 4.1 - A manufactured item is classified as good, a...Ch. 4.2 - Prob. 1ECh. 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 - Determine the correlation coefficient p for each...Ch. 4.2 - Determine the correlation coefficient p for each...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. 11ECh. 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. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - For each of the following functions, determine the...Ch. 4.4 - Using Example 4.4-2, (a) Determine the variances...Ch. 4.4 - Let f(x,y)=43,0x1,x3y1, zero elsewhere. (a) Sketch...Ch. 4.4 - Using the background of Example 4.44, calculate...Ch. 4.4 - Two construction companies make bids of X and Y...Ch. 4.4 - Let T1 and T2 be random times for a company to...Ch. 4.4 - Let X and Y have the joint pdf f(x,y)=cx(1y),0y1,...Ch. 4.4 - Show that in the bivariate situation, E is a...Ch. 4.4 - Let x and y be random variables of the continuous...Ch. 4.4 - Let X and Y be random variables of the continuo us...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Let f(x,y)=18,0y4,yxy+2, be the joint pdf of X and...Ch. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Let X have the uniform distribution U(0,1), and...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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- ox² = 3, or² = 5, oxy = 2, Z = 2Y – 4X – 2 a. Determine the variance of Z.arrow_forwardExpress var(X + Y), var(X − Y), and cov(X + Y, X −Y) in terms of the variances and covariance of Xand Y.arrow_forwardLet X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?arrow_forward
- (Math 161A/163 review) Suppose that X₁, X2, X3 are independent Exponential (A) random variables. A> 0 and r> 0 are constants. Find the mean and variance of Y where Y = 2(X₁+rX2 - X3)arrow_forwardDonarrow_forwardIf X1, X2, and X3 are independent and have the means4, 9, and 3 and the variances 3, 7, and 5, find the mean andthe variance of(a) Y = 2X1 − 3X2 + 4X3;(b) Z = X1 + 2X2 − X3.arrow_forward
- IQ tests supposedly measure our intelligence. They typically are ‘normed’ so that they have a mean of 100 and a standard deviation of 15. (Higher scores show higher intelligence.) Use the graph and use the z-score and percents from columns b and c in Table A, when relevant. If you scored 132, what is your z-score? (Interpret.) Use table A X, z(a), (b), and (c) X z (a) (b) (c) and use the graph! Write down or save your response to use in Part 2 of this quiz. Group of answer choices -2.53 z. I'm at the 98.34 percentile rank and 1.66% of people scored smarter than me. 2.13 z. I'm at the 98.34 percentile rank and 1.66% of people scored smarter than me. -2.13 z. I'm at the 1.66 percentile rank and 98.34% of people scored smarter than me. 2.53 z. I'm at the 0.57 percentile rank and 99.43% of people scored smarter than me. 2.13 z. I'm at the 1.66 percentile rank and 98.34% of people scored smarter than me. 2.53 z. I'm at the 99.43 percentile rank…arrow_forwardThe mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter A. The mean of T= -3x +20 is ___ B. The mean of W= Y - X is ___ C. The variance of D = X - 2Y is ___arrow_forwardx² + + 1,0 < x < 1,0 < y < 2, 0, elsewhere. (x + 1/3), h(y)= 1/3 +y/6. g. Determine the variance of X². Determine the variance of Y² h. f(x, y) = g(x)=2xarrow_forward
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