* The waiting time T (in hours) between each SMS you receive is random with the density function. f(t)=1,8e-1,8t , t2 0 1- Find the expected time between SMS and find the corresponding variance.
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- Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.Suppose the random variable Y has an exponential distribution with mean 2. Use the method of transformations to find the density function of U=(1/5)Y+3Let the continuous random variable X denote the current measured in a thin copper wire in milliamperes. Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?
- The wait T in hours between every phonecall a person recives is random given the densityfunction f(t) = 1.8e-1.8t for t ≥ 0 Find the expected time between calls and find the variance.A random variable X has probability density function (pdf) fx(x), wherefx(x)= c(1–x4) -1≤x≤1elsewherei)Find the cdf Fx(x)of Xii)Find ciii)Find the variance of X.he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.
- A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. f(x) = 2(x+3)/7, 0<x<1, 0, elsewhere Find the variance of X.For 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.)
- Find the mean and variance for the distribution of random variable X whose density function is f(x). f(x,y)= 1/16x^2e^-x/2 x>0Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability density function of the random variableY = 4X + 4 2-Find the probability P(Y>4).Let Y1 = 0.5, Y2 = 0.25, Y3 = 0.75, Y4 = 0.25 and Y5 = 1.25 be a random sample of width 5 selected from the population with the following probability density function. Which of the following is the estimation value obtained by the moment method for the unknown q parameter of this population?