The continuous random variable X represents the amount in pesos of an Uber trip, which has a density function fx(x) = a(40) a xa+1
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- Let X be exponentially distributed with parameter λ. Calculate the probability density of Y =(X−3)/(X+1). please provide some explanation with the taken steps, thank you in advance.Let X be a continuous random variable with density function fx(x) ((3/2)x?) 1-1.1(X). Find the density function of W=2-X, using the CDF technique.The dealer's profit, in units of $1000, on a new automobile is a random variable X having the density function given by ={2(1-x), 0Find the mean, standard deviation and the median of the density function: f(x)= (6/343)x(7-x) [0,7]The joint density of X and Y is given by, ху, Iw(x, y) = (x² +: 0 l) b) Find the marginal probability distributions of X and Y. c) Find the conditional probability density function of Y given X=0.5 and calculate P(YAn insurer's annual weather related loss, X, is a random variable with density function f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise. Calculate the 30th percentiles of X. (Round to 2 decimals).At a restaurant, the density function for the time a customer has to wait before being seated is given by f(t) = 2e¯ if t > 0. Find the probability that a customer will have to wait at least 6 minutes for a table. Probability = .000006 -2tThe random variable Y is defined by Y = - (X + \X1), where X is another RV. %3D Determine the density and distribution function of Y in terms of those of X. 44A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tonsSuppose that the random variable X has density function fx (x) = bx°-1 for 0 < x < 1, where b is a constant. If the median of X is 0.4, what is the value of the constant b?Consider the probability density fx (x) = a. eb x! where X is random variable whose allowable values range from x = -o to + o. Find (a) the CDF (b) the relation between a and b (c) the probability that x lies between 1 and 2.Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.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