(9) If X is a continuous random variable with p.d. f. f(x) = 6 +12,0 ≤x≤3 ,othewise The probability density function of Y= 5x + 3 is:
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- suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)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?
- A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 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.)Find the conditional expectation E(Y/X=0.47) if the joint probability density function of the random variable X and Y isf(x, y) = 1/x, 0 < y ≤ x ≤ 1.
- Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?Please answer the question as quickly as possible Suppose a continuous random variable X has the probability density function f(x) = 2e^(−2x), x ≥ 0. Compute the expected value of the random variable Y = 2X − 1.If X ~ U(3, 15), what is the probability density function for this distribution?
- 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.What is the variance of a continuous probability distribution function with the probability density function f(x) = 4(x-1)^2 for 0 < x < 2?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, (−∞,∞)
