Part4 Let X and Y be jointly continuous random variables with joint density fx,y(x,y) = i(x+ 3y)e-(x+y) for a > 0 and y > 0, 0 , otherwise. Determine P(X > Y) to 2 decimal places. Part5 Let X be a continuous random variable with log-normal distribution, i.e. fx(x) = IV27 =e - 7 ( log x) 2 for r > 0, 0 , otherwise. Determine the value of A = v2TE[| log X"]]. Part6 Let X be a continuous random variable with probability density function given by fx(x) = 1(1 -x2) for r E (-1, 1), 0 , otherwise. Compute the variance of X to 1 decimal place. Part7 Let X and Y be jointly continuous random variables with joint density 3(x+y) fx,x(x, y) = o. for r E (0, 1) and y E (0, 2), otherwise. Compute E[sin(7 XY)] to 2 decimal places. Part7 Let X1, ..., X10 be independent discrete random variables such that for all n = 1, . .. . 10, for k = 0, for k = 1, PXn (k) = for k = 2, for k = 3. Consider the random variable 10 Y = Xn . n=1 Compute EY] To 3 decimal places