The probability density function for the continuous random variable X is given by: (A(x² f (x) = - 2x + 21) 0
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- The probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0Q2\ Consider is a continuous random variable with probability density function given by: Find: 1- P(50Find 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) 0The probability density function of the Pareto distribution is given as: f(x) =- (x>0) (1+x)*1 Show that: Var(x) = ( α- 1), (α-2)A continuous random variable X is defined by f ( x ) = (3+x)^2/16 ; -3<x<-1 f(x) = = ( 6 - 2x^2)/16 ; -1<x<1 f(x) = ( 3 - x^2)/16 ; -1<x<3 a. Verify that f(x) is density b. find the meanthe probability density function for the waiting time was given by f(x) = 0 for x 15 a) Find the expected value of the waiting time, X minutes. b) Find the variance and standard deviation of the waiting time. c) What is the probability that the waiting time is within two standard devia- tions of its expected mean value? 1 15I need help with this probability density function problem. It asks to calculate the probability that the battery lasts longer than 1 hour. Please show work so that I can understand future problems like this.The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 < x<1 f(x) = - 0, 5 elswhere Find the stàndard deviation of above stated continuous random variable (X)Recommended 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