15.3 Exercise 6

(See Exercise 21 from "Problems on Conditional Expectation, Regression") A number X is selected randomly from the integers 1 through 100. Each of two people draw X times independently and randomly a number from 1 to 10. Let Y be the number of matches (i.e., both draw ones, both draw twos, etc.). Determine the distribution for Y. Determine $E \left[Y\right]$ and $P \left(Y \leq 10\right)$.