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 of the 'x' continuous chance variable is as shown in the figure. So what is P (X> 30)?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(50* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.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) 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)the 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 15The 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