1. The joint density for the random variables (X, Y) is given below. 2(r+2y) for 0
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![1. The joint density for the random variables (X, Y) is given below.
2(x+2y)
for 0<I<1,0<y<1
f(r,u) =
for clsewhere
(a) Find the marginal density of X
(b) Find the marginal density of Y
(c) Find Var[X]
(d) Find Var[Y]
(c) Are X and Y statistically independent?
(f) Find P(X > 0.6)
(g) If E[XY]=0.8, find the corrclation between X and Y
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- The continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 1. y2' Calculate the probability P(X < 0.5, Y < 2)Consider two continuous random variables X and Y with marginal distributions g(x) and h(y)respectively and the joint density function given by: x > 0, 0 < y < 2 elsewhere. f (r.y) Then: X and Y ar statistically dependent f(x,y)#g(x)h(y) None of these f(ylx)=g(x)X and Y are independent variables, which distribution is given by is given by the functions: (picture) Determine the density of random vector (X,Y)' Determine F(5,2) Determine P(Y>2X) and sketch the picture
- 4. Let X and Y be independent, continuous random variables with densities and fx(x) = = fy (y) = = 0 {} if 0 < x < 2 otherwise. y if 027. If the joint density of the random variables X and Y is [emin{x,y) - 1] e-(x+y) if 0 < x, y <∞ f(x, y) = 0 otherwise, then what is the marginal density function of X, where nonzero?Please helpPlease do only defg1. The joint density for the random variables (X, Y) is given below. for 0SS1,0SySI 0. for clsewhere (a) Find the marginal density of X (b) Find the marginal density of Y (c) Find VarlX] (d) Find VarV] (e) Are X and Y statistically independent? () Find P(X>0.6) (R) I EXY-0.8, find the correlation between X and YLet the random variable X have'the marginal density 1 f, (x)= 1, 1Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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