Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally distributed with a mean of 98 cm and a standard deviation of 2 cm.

1. Find the mean perimeter of the trapezoid.

2. Suppose X1, X2, and X3 are independent of each other. Find the variance of the perimeter of the trapezoid.

3. Suppose that the covariance between X1 and X2 is 35, but X3 is independent of both X1 and X2. Find the variance of the perimeter of the trapezoid.

Expert Solution

orchestra answered 1 year ago

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally distributed with a mean of 98 cm and a standard deviation of 2 cm. 1. Find the mean perimeter of the trapezoid. 2. Suppose X1;X2; and...

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Question

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

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