20. The quantity demanded (in thousands of pounds) of a Red Farms Butter each week is a contniuouis1 1 236random variable with probability density function (PDF): f(x)=x -x² (0≤x≤6).a) Show that it is a PDF on the specified interval.b) What is the probability that between 3-4 thousand pounds of butter will be demanded in a randomlyselected week?

Answered: Image /qna-images/answer/e6266f8e-57b9-4521-a258-d224b63a26eb.jpg

Answered: 20. The quantity demanded (in thousands…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value? i) What is the expected value of X4?
certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
a survey of 100 online shoppers at a certain popular web store reveals the following probability distribution of the number of items purchased per visit. assume p(x) represents the true pdf and is valid x= 0, 1, 2, 3, 4, 5, 6, 7 f(x)= 0.41 .12 .16 .15 .05 .06 .03 .02 calculate the expected number of items purchased per visit find the probability that the next customer will not make a purchase.
Students arrive at a lecture theatre independently. Suppose the number of students arriving in an hour follows a Poisson distribution with mean 10. Let 7 (in hours) be the time required to wait for 5 students to arrive. Derive the probability density function of T.
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
(d)
A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.

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