# HOMEWORK 4 1. Ross Chapter 2, problems 2, 5, and 8 *Problem 2.2 (...

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Q1
X0 = 11
Xn = (7 ∗ Xn−1 + 3) mode 70
X1 = (7 ∗ X0 + 3) mode 70 = (7 ∗ 11 + 3) mode 70 = 10
X2 = (7 ∗ X1 + 3) mode 70 = (7 ∗ 10 + 3) mode 70 = 73
X3 = (7 ∗ X2 + 3) mode 70 = (7 ∗ 73 + 3) mode 70 = 24
X4 = (7 ∗ X3 + 3) mode 70 = (7 ∗ 24 + 3) mode 70 = 31
X5 = (7 ∗ X3 + 3) mode 70 = (7 ∗ 31 + 3) mode 70 = 10
It cannot be considered as good random generator, as the produced values are not uniformly distributed. The mode value is not a prime number, hence there would be an unqual probability of generating numbers. Hence, next value is dependent on the previous value, hence it is not a good property of random number generators.
There are two properties of a good random number generator:
1. Equal probability of generating numbers.
2. There must be no dependency on previous value in order to generate next value.
Q2
Area under the curve can be estimated by multiplying distance between ‘b’ and ‘a’ and average height of the poles.
Monte Carlo gives, average height 1.99.
Estimated Area is: 1.99 * (3-1) = 3.98...

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