The acceleration due to gravity by dropping a baseball and m

The acceleration due to gravity by dropping a baseball and measuring the time T it takes for the ball to travel a measured vertical distance D is G = 2D/T2. Suppose that both D and T are measured independently with errors so that E(D) = 432 ft, V(D) = 0.01 ft2, E(T) = 5.2 sec and V(T) = 0.004 sec2. Compute approximate values for E(G) and V(G) by propagation of error. What percent of the variance V(G) is due to the uncertainty in measuring the distance D? time T? Suppose that X1 and X2 are independent random variables with E(X1) = 2, E(X2) = 5, V(X1) = 2, V(X2) = 10. Define Y = X1 Times X2. Compute the mean and variance of Y by propagation of error. If X1 and X2 are both distributed Lognormal, what is the distribution of Y? Give a short explanation.

Solution