Please write a full answer and give a good explanation. Do not answer it if you do not know it!

5. Summer exam 2012 Let the continuous random variables X and Y be the length and width of a rectangle. These two random variables are independent of each other and defined as XUnf(0,2), og Y~Unf (0,3). a) What is the expected value of the perimeter of the rectangle? b) What is the variance of the perimeter of the rectangle? c) What is the probability of the area of the rectangle being less than 1? Hint: The joint density of (X, Y) is f(x,y)-1/6 if 0 x 2 and 0 y 3, f(x,y) = 0 otherwise. 5. Summer exam 2012 Let the continuous random variables X and Y be the length and width of a rectangle. These two random variables are independent of each other and defined as XUnf(0,2), og Y~Unf (0,3). a) What is the expected value of the perimeter of the rectangle? b) What is the variance of the perimeter of the rectangle? c) What is the probability of the area of the rectangle being less than 1? Hint: The joint density of (X, Y) is f(x,y)-1/6 if 0 x 2 and 0 y 3, f(x,y) = 0 otherwise