Unformatted text preview: X â€™s. 6. Derive the moment generating function for the exponential distribution with rate Î» . Be sure to include an explantion as to why we need t < Î» . 7. Required for 5520 students only Let X be a continuous random variable with pdf f X ( x ) and let Y = g ( X ) for some continuous invertible function g . Show that E [ g ( X )] = i âˆžâˆž g ( x ) f X ( x ) dx. (Be sure to show the details for the limits of integration!) 8. Required for 5520 students only Let U 1 and U 2 be independent unif (0 , 1) random variables. Show that X 1 and X 2 deÂ±ned as X 1 = âˆš2 ln U 1 cos(2 Ï€U 2 ) X 2 = âˆš2 ln U 1 sin(2 Ï€U 2 ) are independent standard normal random variables....
View
Full Document
 Fall '11
 Manuel
 Normal Distribution, Probability theory, probability density function, iid X1 X1

Click to edit the document details