(✰✰✰✰) Suppose X is a random variable with the probability density p(x) = K = E[X] = 0 Var[X] = K (49 + x2)³ 3' . Find the following:
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![(✰✰✰✰) Suppose X is a random variable with the probability density p(x):
K =
E[X] = 0
Var[X] =
K
Find the following:
(49 + x²)³
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2498a7f5-c5b9-4c1b-a67f-f62ca6767a42%2F6d065ed7-c4de-4d9a-a1e9-5fc35677fc27%2F9ykucun_processed.png&w=3840&q=75)
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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.If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
- Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]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.)
- Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx3; [2, 4]The random variables X and Y have the following joint probability density function:f(x,y)={e−x−y , 0<x<∞; 0, elsewhere. What is Cov(X,Y)(X,Y)?Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) = kx; [0, 3]
- Let f(x) = k(3x − x2) if 0 ≤ x ≤ 3 and f(x) = 0 if x < 0 or x > 3. (a) For what value of k is f a probability density function? k = (b) For that value of k, find P(X > 1). P(X > 1) = (c) Find the mean. ? =suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)Suppose that the random variables X, Y , and Z have the joint probability density function f(x,y,z)=cxyz for 0 < x < 1, 0 < y < 1, and 0 < z < 1. Find the E(x). Use the Scientific Method of Answering (Given, Required, Formula and Solution.)