The joint density function for a pair of random variables X and Y is given. (Round your answers to four decimal places.)(cx(1 + y)0f(x, y)=(a) Find the value of the constant C.(b) Find P(X ≤ 1, Y≤ 1).if 0 ≤ x ≤ 4,0 ≤ y ≤ 2otherwise(c) Find P(X + Y ≤ 1).

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Answered: The joint density function for a pair…

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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For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
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The joint density function for a pair of random variables X and Y is given. [cx(1 + y) f(x, y) if 0 ≤ x ≤ 4,0 ≤ y ≤2 otherwise