1. Is the following distribution a probability distribution? (x, P(X)) = (-2,1.23); (-1, 0.15) ; (0, -1.20); (1, 0.52); (2, 0.30) There are five ordered pairs: X values and their probabilities for example P(1) = 0.52. X -2 , -1 , 0 , 1, 2 P(X) 1.23, 0.15, -1.20, 0.52, 0.30 2. A coin is tossed 11 times. Find the probability of getting exactly three heads. Use the binomial theorem X= 3 and n=11 3. A discrete probability distribution consists of the finite number of variables a random variable can assume and the corresponding probabilities of the values. 4. If 5% of the bolts made by an automotive factory are defective , what is the probability that in a shipment of 200 bolts, there are 15 defective bolts? 5. If a gambler rolls three dice and gets a sum of 10, the gambler wins $20, and if the gambler gets a sum of three they win $10. The cost to play the game is $5. What is the expectation ( expected value) of this game? 6. A school is sending 15 children to a camp. If 30% of the children in the school are first graders, and the 15 children are selected at random from among all 6 grades at the school, find the mean and the variance of the number of first graders chosen. 7. In a survey, 80% of the voters support a particular referendum. If 30 voters are chosen, find the standard deviation of the number of voters who support the referendum. 8. Find the mean of the distribution shown below: (X,P(X) = (1,0.58); (3, 0.42) X 1 , 3 P(X) 0.58, 0.42