1) Perform a random number simulation of a biased coin n times, where n is usually a very large positive integer. Determine the value of n for each of the cases (@), (b) and (c) such that the probability of head and tail is very close to (a) (0.7, 0.3) (b) (0.8, 0.2) (c) (0.9, 0.1) up to 5 decimal places.
2) Assume that the biased dice is rolled once. Perform a random number simulation of this biased dice n times, where n is usually a very large positive integer. Determine the value of n for each of the two cases:
(@) (0.2, 0.1, 0.15, 0.15, 0.2, 0.2) and
(b) (0.1, 0.1, 0.1, 0.2, 0.25, 0.25).
where the individual scalars in the above two vectors represent the probabilities of occurrence of the number "", "2". ...."6" on the dice.
3) Consider the "pi" problem discussed in our class today. Determine the number of throws necessary (n) such that the simulated value of pi becomes equal to 3.14159 exactly. [Note: You need to determine the number of times the points fall on or inside the circle of radius 1]
4) Perform the Up-Down sequence problem for any guess number randomly generated between 1 and 1000000. Plot the value of the number generated against the number of iterations you need to go until you reach the value 1.