probability density
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A:
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Q: continue the question
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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.Let the density function of random variable x be given by fx(x) =0x^0-1, 0<x<1 Suppose x1, x2.. Xn be random sample taken from above population. Define an estimator with=-log(xi) here the new random variable with follows1. A continuous random variable X has the following pdf: 2. Let X be a continuous random variable with density function
- 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.)If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.- If we assume that the moment of death of a tilapia fish in one of the commercial ponds for selling fish is Random and regular on the time period [300,0] where time is measured in minutes. So what is it Prospect 1. That the moment of death of this fish is more than three hours 2- This fish should live less than three hours 3- Find the density function, then find the expectation and variance
- 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>01. A random variable Y has a probability density function f(y) = A(y − 1.5) over the state space −2 ≤ y ≤ 3, where A is a constant. Calculate the median of the random variable Y. 2. Suppose the lifetime of a particular type of old mobile, X, can be modelled by the probability density function f(x) = 0.5 e −0.5 x; x ≥ 0. Suppose that you just bought 5 old mobiles, what is the probability that at least 3 of the mobiles will survive less than 2 years?1. A continuous random variable X has a probability density function (PDF) p(x) = k( 8-x^2/2) on the interval [0, 4] (a) Find k such that p(x) is a valid PDF. (b) Find P(X ≤ 1). (c) Find the mean, µ, of X. (d) Find the variance, σ 2 , of X.