The joint density function of the random variables X and Y is: 0
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A: A joint probability density function is given by,
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A: by integrating the pdf function we can find out the probability
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A: Introduction :
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Q: 4. The shelf life in days, for bottles of a certain prescribed medicine is a random variable having…
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Q: The joint density function of the random variables X and Y is: (6x, f(x, y) = {° 0 0/30 |Y-0.50). (2…
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A: The given pdf is as follows:
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- Situation. P(X>0.30) Y =0.50 The joint density of the random variable x and y is f(x-y)={6x, ; 0<x<1 ; 0<y<1=x 0, elsewhere Please answer asapb) Given the following density function of the random variable X: f(x) = (1+x)2, 0<x<1 = 0, Find E(X) and V(X).x~n(0,1) and find the probability density function of the random variable y=|x|
- The joint probability density function of two random variables X and Y is f(x, y)= 4xye^-(x^2+y^2). Find P(1<x<=2, 1<Y<=2)If the joint probability density function of two continuous random variables X and Y isgiven byf(x; y) = 2, 0 < y < 3x, 0 < x < 1; find(a) f(yjx),(b) E(Y jx),(c) Var(Y jx).The joint density function of random variables X and Y is given as follows: Find: (a) P{Y > 2} (b) P{1 < X + Y < 3}
- 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.)2. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)Since P{X=1}=P{X=2}=P{X=3}=0.2 , P {X=4}=0.4 , plot the probability density function of the random variable X and the distribution function.
- A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X the proportion of time that the drive-up facility is in use and Y the proportion of time that the walk-up window is in use. Suppose that the joint density function of these random variables is f(x,y)={65(x+y2) 0≤x≤1,0≤y≤10 elsewhere Find P(X>14,Y≤13) ((p. 385 # 13). Find the density of Z = X − Y for independent Exp(λ) randomvariables X and Y .A random variable X has probability density function (pdf) fx(x), where fx(X)= c(1–x4) -1≤x≤1 i) Find cii) Find cdf Fx(x) of Xiii) Find the variance of X.iv)Find P [│X│ < 1/2]
