Data structures and Algorithm Analysis

1. In the probability review in class, we showed an easier way to compute the Expected value (average) of the sum of two dice, by using the Linearity of Expectations. (a) Show how you would use the Linearity of Expectations property to compute the Expected value (average) of the sum of 10 fair dice. (b) Do the same, but now compute the Expected value (average) of the sum of 10 biased dice in which the probability of obtaining value 6 is 1 and the probability of all other values are 0. Show all your steps of using Expectations and Linearity of Expectations.

(10 points)

2. In the randomized hiring problem, (a) What is the probability that the first candidate is hired?

(b) what is the probability that the fifth candidate is hired? Explain your answers.

(10 points)