Let Y = X1 + X2 + 2X3 represent the perimeter of an isoscelestrapezoid, where X1 is normally distributed with a mean of 113 cmand a standard deviation of 5 cm, X2 is normally distributed with amean of 245 cm and a standard deviation of 10 cm, and X3 isnormally distributed with a mean of 98 cm and a standard deviationof 2 cm.
1. Find the mean perimeter of the trapezoid.
2. Suppose X1, X2, and X3 are independent of each other. Findthe variance of the perimeter of the trapezoid.
3. Suppose that the covariance between X1 and X2 is 35, but X3is independent of both X1 and X2. Find the variance of theperimeter of the trapezoid.
