Calculus: An Applied Approach (MindTap Course List)
10th Edition
ISBN: 9781305860919
Author: Ron Larson
Publisher: Cengage Learning
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Question
Chapter 9, Problem 33RE
To determine
To graph: The probability density function
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Using the uniform probability density function:U
f(x)=1-(b-a) for a<=x<=b
0 elsewhere
The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:f(x) = 8 for 11.975 ≤ x ≤ 12.100andf(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?c. Quality control accepts production that is within .02 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?
PROOF
Let X and Y be continuous random variables with joint distribution function, F (x,y).
Let g (X,Y) and h (X,Y) be functions of X and Y.
PROVE
E[cg(X,Y)] = cE[g(X,Y)]
Proof
Let X and Y be independent integrable random variables on a probability space and f be a nonnegative convex function. Show that E[f(X +Y)] ≥ E[f(X +EY)].
Chapter 9 Solutions
Calculus: An Applied Approach (MindTap Course List)
Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CPCh. 9.1 - Prob. 3CPCh. 9.1 - Prob. 4CPCh. 9.1 - Prob. 5CPCh. 9.1 - Prob. 6CPCh. 9.1 - Prob. 1SWUCh. 9.1 - Prob. 2SWUCh. 9.1 - Prob. 3SWUCh. 9.1 - Prob. 4SWU
Ch. 9.1 - Prob. 5SWUCh. 9.1 - Prob. 6SWUCh. 9.1 - Prob. 7SWUCh. 9.1 - Prob. 8SWUCh. 9.1 - Prob. 9SWUCh. 9.1 - Prob. 10SWUCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10ECh. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Children The table shows the probability...Ch. 9.1 - Prob. 21ECh. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Baseball A baseball fan examined the record of a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.2 - Prob. 1CPCh. 9.2 - Prob. 2CPCh. 9.2 - Prob. 3CPCh. 9.2 - Prob. 4CPCh. 9.2 - Prob. 5CPCh. 9.2 - Prob. 1SWUCh. 9.2 - Prob. 2SWUCh. 9.2 - Prob. 3SWUCh. 9.2 - Prob. 4SWUCh. 9.2 - Prob. 5SWUCh. 9.2 - Prob. 6SWUCh. 9.2 - Prob. 7SWUCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 34ECh. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Prob. 39ECh. 9.3 - Prob. 1CPCh. 9.3 - Find the variance and standard deviation of the...Ch. 9.3 - Use a symbolic integration utility to find the...Ch. 9.3 - Prob. 4CPCh. 9.3 - Prob. 5CPCh. 9.3 - Prob. 6CPCh. 9.3 - Prob. 7CPCh. 9.3 - Prob. 1SWUCh. 9.3 - Prob. 2SWUCh. 9.3 - Prob. 3SWUCh. 9.3 - Prob. 4SWUCh. 9.3 - Prob. 5SWUCh. 9.3 - Prob. 6SWUCh. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 13ECh. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Prob. 15ECh. 9.3 - Using two Methods In Exercises 1316, find the...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Consumer Trends The number of coupons x used by a...Ch. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Transportation The arrival time t (in minutes) of...Ch. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - License Renewal The waiting time t (in minutes) at...Ch. 9.3 - Demand The daily demand x for a certain product...Ch. 9.3 - Prob. 48ECh. 9.3 - Demand The daily demand x for water (in millions...Ch. 9.3 - Prob. 50ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Education For high school graduates from 2012...Ch. 9.3 - Prob. 57ECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Revenue A publishing company introduces a new...Ch. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 1TYSCh. 9 - Prob. 2TYSCh. 9 - Prob. 3TYSCh. 9 - Prob. 4TYSCh. 9 - Prob. 5TYSCh. 9 - Prob. 6TYSCh. 9 - Prob. 7TYSCh. 9 - Prob. 8TYSCh. 9 - Prob. 9TYSCh. 9 - Prob. 10TYSCh. 9 - Prob. 11TYSCh. 9 - Prob. 12TYSCh. 9 - Prob. 13TYSCh. 9 - Prob. 14TYSCh. 9 - Prob. 15TYSCh. 9 - Prob. 16TYS
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
Using the uniform probability density function shown in Figure, find the probability that the random variable X is between 1.0 and 1.9.
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PROOF
Let X and Y be continuous random variables with joint distribution function, F (x,y).
Let g (X,Y) and h (X,Y) be functions of X and Y.
PROVE
If X and Y are independent, then E[XY] = E[X] E[Y]
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PROOF
Let X and Y be continuous random variables with joint distribution function, F (x,y).
Let g (X,Y) and h (X,Y) be functions of X and Y.
PROVE
E[g(X,Y) + h(X,Y)] = E[g(X,Y)] + E[h(X,Y)]
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a) Find the conditional probability density function under the condition A = {X> 1/8}.b) Find the domain of the function.
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a) Find the conditional probability density function under the condition A = {X> 1/8}.b) Find the domain of the function.c) Find the conditional expected value of X.
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PROOF
Let X and Y be continuous random variables with joint distribution function, F (x,y).
Let g (X,Y) and h (X,Y) be functions of X and Y.
PROVE
If X = Y, then Cov(X,Y) = Var(Y)
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use a graphing utility to graph the function. Determine whether the function f represents a probability density function over the given interval. If f is not a probability density function, identity the conditions that is (are) not satisfied
f(x)= 1/8 (0,8)
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The probability density of a random variable X is given in the figure below.
From this density, the probability that X is between 0.6 and 1.4 is:
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Proof
Let X and Y be integrable random variables on the probability space (Ω,F,P)andA⊂Fbe a σ-field. Show that E[YE(X|A)] = E[XE(Y|A)], assuming that both integrals exist.
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One of the important properties of the probability density function , f(x) , of a random variable X is f(x) >= 0 , for all values of X.
A) true
B) false
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The probability density of a random variable X is given in the figure below.
From this density, the probability that X is at least 1.42 is:
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