The joint density of X and Y is given byf (x, y) = 1 2eye(xy)2/2 0 < y < q,q < x < q (a) Compute the joint moment generating functionof X and Y.(b) Compute the individual moment generatingfunctions.
Color Coding: Topics MINITAB Examples STT 351 Notes Normal −1 2 f x = 1 e 2 x ( ) 2Π inf < x < inf √ To find probabilities between two points (a,b] we have to integrate this function between a,b. Using MINITAB: 1) Calc 2) Probability distribution 3) Normal (mean = 0, Standard deviation = 1) 4) Select cumulative probability This will give the area under the curve up to the point x For any a value, the area under the curve up to the point a is = P(X ≤ a) # If we want to find the area under the curve between two points we can use the equation….. P( a < X ≤ b ) = P( X ≤ b ) – P( X ≤ a ) Using MINITAB: To find
