Suppose that (X,Y)' has a density function given by for a > 1, y > 0, f(x, y) 10, otherwise. Determine the distribution of X?Y.
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- The random vector (X,Y) has the following joint probability density function:f(X,Y)(x,y) ={4xye−(x^2+y^2), x >0, y >0, 0, otherwise LetZ=√(X2+Y2) Find the probability density of the random variableZ.A continuous random variable has density function (Зx2 for 0 0. The ratio of the mode of this distribution to the median is:There are two components in an electronic system. Let X and Y denote the lengths of life in years. The joint density function of these variables f(x, y) = {ye-&+x) ,x 2 0, y Determine P(x>3) What is the probability that both components will exceed 3 years?
- 2. An investor's losses follow a distribution with density function, f(x) =, x > 1 and 0 everywhere else, To recover her losses, the investor purchases an insurance policy with a deductible of $1. Show that the insurance company will go bankrupt. Hint: The expected amount of the losses paid by the company is too large.Do correctly and completely...thank u Need asapplease use the density of X. Find PDF of exp distribution and then plug it into E(e^tX).
- 46. Given that X has a density function 2x 3- x f (x) = for 0Calculate the mass of the straight wire from x = 0 to x = , where as the density function is p(x) = tan (; x) %3DNow, assume that Y₁,..., Yn distributed iid, each with density -{* where is positive constant. Find the density function for fy) (y). fy(y) = e-(-0), 0, if y> 0; otherwise,A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 0The life time, in years, of some electronic component is a continuous variable with the density f(x) = ) = - (a) Find k. (b) Find cdf F(X). x/x7, 0, x ≥ 1 x < 1 OCSuppose X and Y have joint density f(x,y)=10x2y, 0<y<x<1. Find the marginal density of X.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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