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Find the median of the random variable whose density function is
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- Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.arrow_forwardLet X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.arrow_forwardSuppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?arrow_forward
- Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.arrow_forwarda. The probability density function for X is f(x) = e=x , x > 0, zero, e.w. Find the probability density function of Y = (Use CDF Technique) b. Suppose that X1 ~b(5,) and X2~b(7,) are independent random variables. Let Z = X1 + X2 + 7, show that Z~b(12,). (Use MGF method)arrow_forwardthe popularity density function f(x) for a uniform random variable X defined over the interval [2,10] is?arrow_forward
- Let X be a random variable with density function - 1< x < 2, fn) = fx*/3, f(x) = 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3.arrow_forwardFor 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.)arrow_forwardSuppose that the random variable X has density fx (x) = 4x³ for 0 X).arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt