A random variable X has the density function: fx (x) = { 3 (3-x) 1
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A: The pdf of random variable X is given: fX(x) = θ xθ-1, 0≤x≤1
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Q: function fx,y given by Suppose that X and Y have a joint probability density -{..-* fxy(x, y) =…
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A: Given, The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x…
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Q: b) Find the marginal probability density function of X, fy(x).
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Q: 2. find the density function with X and 0, i.e. g(x|0)
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Q: A random variable X has a probability density function 0; x < 0, 0≤x≤1, 1<x<∞0. f(x)= { 22
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A: Introduction :
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Q: The probability density function of a random variable is kVx+ – 1 f(x) - if 1 s x< 2
A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…
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- The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?The joint density function of the random variables X and Y isSuppose random variable X has a density function f ( x ) = { 2 /x 2 , 1 ≤ x ≤ 2 0 , o t h e r w i s e . Then E[X4] =?
- Find the mean and variance for the distribution of random variable X whose density function is f(x). f(x,y)= 1/16x^2e^-x/2 x>0For 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, (−∞,∞)
- Consider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the lifetime of a bulb is f(t)=14e−t/4,t≥0.What is the probability that the bulb will fail within 5 hours?
- The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. What is P(X ≤ 4)? What is P(4.5 < X)?The joint probability density function of random variable X and Y is given by: f(x,y) = {e^-y, if 0<x<y<∞ 0, otherwise}LEt Z=X+Y, Find the probability density function of Z.