Let X and Y be independent standard normal random variables. Consider the transformation U = X + Y and V = X-Y. a. Use the theory of distributions of functions of random variables (Jacobian) to find the joint pdf of U and V. Are U and V independent? Why? What is the distribution of U and the distribution of V?
b. Use moment generating functions to answer question (a).

Find the value of the cosine for angle a

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function. how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

Apool measures 100 meters by 100 meters a toddler inside the pool and trows a ball 60 centimeters from one edge of the pool. how far is the ball from the opposite edge of the pool