b) Suppose that X is a random variable with the probability density function given by (2(1-x),0 ≤ x ≤ 1 otherwise f(x) = {20₁ Find the density function of W = 2X-1 using method of cumulative distribution function.
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![b) Suppose that X is a random variable with the probability density function given by
f(x) = {2(1-
(2(1-x), 0≤x≤1
otherwise
Find the density function of W = 2X - 1 using method of cumulative distribution
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- A continuous random variable T (in years) of the lifespan of a device has the following probability density function f (t) = {3 pt", Osts2 otherwise where p is a constant, (a) Determine the value of p. (b) Find the cumulative distribution function of T, F(t). (c) If U =ÉT+1 determine E(U) and Var(U).X is a random variable whose cumulative distribution function F(x) satisfies F(1) = 13, F(2) = 34, and F(3) = 1 • Make X discrete and give its probability mass function.• Make X continuous and give its probability density function.What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?
- Let X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . . . , pn}. The entropyof the random variable is defined asH(X) = −Σpilog (pi) Find the probability mass function for the above discrete random variable that maximizes the entropy.Find the expected value of the continuous random variable g(x)= x^2+3x+2, if the density function for random variable x are shown in the following equation. f() = [F(2x-1) 0Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.Let X1, X2,...,X, be a random sample from a distribution with density function e if x > 0 f(x; 0) elsewhere What is the maximum likelihood estimator of 0 ?Determine the probability density function of the random variable X* if x 1 ON|30A machine has a useful life of 4 to 9 years, and its life (in years) has a probability density function defined by f(x) = 1 1 Find the probability that the useful life of such a machine selected 15 at random will be longer than 7 years?Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-8x - 5y, 0 0).Let X will be continuous random variable with probability density function as below. f(x) = {4x , (0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON