Probability and Statistics

Can you please answer these questions below and PLEASE show your work. thank you

All of the problems concern the following situation. It's raining on a soccer field. The field is 100 meters long and 70 meters wide. Model the event of a raindrop falling as a randomly selected point in the rectangle pictured.

Consider the following random variables: X is the x-coordinate where a raindrop falls, Y is the y-coordinate of where a raindrop falls, and Z=X+Y.

Soccer Field 70 - 601 501 40! 30 20 101 20 40 60 80 100Which one of the following statements are true? * O X and Y are independent O X and Z are independent 0 Y and Z are independent What is the standard deviation of X? * Q o=50/\\/3 O 0:100/12 carefully compute the cumulative distribution function F(c) = P(Z