The joint probability density function of two dimensional random variable(X,Y) is given 8. xy, 13xsys2 by f(x, y) = - 0, elsewhere Find the marginal density functions of X %3D and Y.
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- If X is continuous random variable then the first moment about the origin is defined to be E (X) = Jxf(x)dx ylgn ihiaasapA random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is given by: ´ayf f(y) = {ya+1 (0, if y > yo elsewhere ii) ayg (a-2)(a-1)2" Show whether or not that the variance of Y is
- 1 Random variables X' and Y'have the joint density fx., (x, y) = 4, 01) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Do last two partThe density function, ху fy(x, y) = f(x) =9 0, 0The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by 2e-(x+2y) X> 0, γ> 0 fx,ylx,v) = { else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.7772 b. 0.3935 10 c. 0.606 d. 0.6318 e. 0.3669A random variable Y have a distribution with parameter a > 0 and y, > 0 if its density function is given by: (ay“ if y> yo fV) = ya+T (0, elsewhere i) Derive the mean of Y. Show all necessary steps. ay (a-2)(a-1)²' ii) Show whether or not that the variance of Y is ·Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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