2.5.8 The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Y measures the acidity of the solution. They have a joint probability density function f(x, y) — А(20 -х — 2у) for 0
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2.5.8 The random variable X measures the concentration of
ethanol in a chemical solution, and the random variable Y
measures the acidity of the solution. They have a joint
probability density
f(x, y) = A(20 - x - 2y)
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- A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.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.)Can I have detailed, step by step explanation for obtaining the answer of the following question? Let Y1 and Y2 have joint density function given by, f(y1, y2) =3(y1) ; 0 <= (y2) <= (y1) <= 1 or 0 ; otherwise Find Cov(Y1, Y2) and correlation coefficient(P).
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