6. Find the expectation E(X) = and variance for the following distributions: (1) (ii) X f(x) 2 1 4 X 2 f(x) 0.1 5 1 2 10 1 4 3 4 5 0.2 0.3 0.4 7. A fair die is thrown. Create the distribution, determine the expectation, and variance for the random variable which represents the occurrence of twice the number appeared. Page 5 of 6 8. A pair of fair dice is tossed. Calculate the mean, variance, and standard deviation for the random variable that assigns the maximum numbers occurs on a pair of dice. 9. Mustafa rolled a fair die. He wins the OMR if even number occurs, and losses for the occurrence of non-even number. Determine, whether the game is supportive to Mustafa by computing expectations. 10. 12 marbles, including 3 red and 9 blue, are included in a box. Three red marbles are randomly chosen as a sample. The expectation E of receiving red marbles can be found.