1. A coin is tossed 5 times. Let X count the number of heads tossed. Determine 2. A coin is tossed 3 times and then a die is rolled. Let spots on the die. Determine , X (HHT 6) X (TTT 4) 3. A red die is rolled and then a green die. Let X (3,4) and X (4,3) 4. Determine f (x) and X X (HHTHT ) . be the number of heads times the number of X (HTT 3) . X 5(Spots on Red) (Spots on Green) . Determine . for the random variable in problem 1. 5. Determine the pmf for the random variable in problem 2. 6. Two dice are to be rolled. Let X be the largest value you see. Determine the distribution of X 7. The collection of values that our random variable assigns non-zero probability is called? 8. Suppose that our random variable 9. Suppose that our random variable X X has pmf has pmf f (x) cx for f (x) c(.3x ) x 1,2,3,4 for . Determine the value of c. x 1,2,L , determine the value of c. 10. Determine the value of c that makes the table below a pmf. x f(x) 1 .16 2 .05 3 .06 4 c 5 .08 11. Given the table of the pmf for a random variable, determine x f(x) 1 .3 2 .05 3 .06 4 .13 F (x) 6 .02 7 .22 8 .14 6 .02 7 .28 8 .08 6 .02 7 .23 8 .08 . 5 .08 12. Given the table of the pmf for a random variable, determine the CDF. x f(x) 1 .2 2 .05 3 .16 4 .23 5 .03 13. The CDF of a random variable the support of X is x 1,2,3,L X is x 1,2,L , c is given the function . Determine 14. The CDF of a random variable support of X X P( X 1) cx 2 F (x) 2 3x x on the support of X , where . is given the function F ( x) 2 x 25 on the support of X , where the . Determine the value of c. 15. The CDF of a random variable is given below. x F ( x) Determine 1 .3 a) d) 2 .05 P( X 5) P(2 X ) 3 .06 b) e) 4 .13 P( X 3) P(3 X 7) 5 .08 6 .02 c) f) 7 .28 8 .08 P(6 X ) P(3 X 7) g) P( X 4.5)