Let 1/9 < c < 1/9 be a constant. Let p(x, y), the joint probability mass function of the random variables X and Y , be given by the following table: y x 1 0 1 1 1/9 1/9 c 1/9 + c 0 1/9 + c 1/9 1/9 c 1 1/9 c 1/9 + c 1/9 (a) Show that the probability mass function of X+Y is the convolution function of the probability mass functions of X and Y for all c. (b) Show that X and Y are independent if and only if c = 0.

Section 6: Statistics in Sports Stat 2220, Espey ➢ Random Variable: a variable with different outcomes that each assume a numerical value ○ Represented with Y ○ Discrete RV: countable ○ Continuous RV: measured on a continuous scale (decimals can be used) ➢ Binomial Random Variable: How many times one two possible outcomes occurs after...