- What is Simulation?
(5 marks) - Define “Random Numbers”.
(5 marks)
3.
a) Statement: Let � be a uniform (0,1) random variable. For any continuous
distribution function �, the random variable � defined by
� = �−1(�)
has distribution function �.
Prove the above statement.
(7 marks)
b) If � is an exponential random variables with rate 1, then its distribution function
is given by
�(�) = 1 − �−�.
Show that
� = − ln(1 − �).
(8 marks)
Question Two: (25 marks) - Explain the rejection method.
(7 marks) - Use the rejection method to generate a random variable having density function
�(�) = ��
1
2⁄ �−�, � > 0
where
� = 1
� (
3
2)
= 2
√�
.
Assignment Mr Hamuth Mohamad Farouk
Page 3 of 5
QUAN 1202
(18 marks)
Question Three: (25 marks) - Explain the term “Monte Carlo Simulation” and explain how it is helpful in decision
making.
(3+3=6 marks) - Use the mixed congruential method with seed 26 constant multiply 17 increment
45 and modulus100. To generate 10 uniformly distributed random variables on
(0,1).
(5 marks) - Use inverse transform method to generate a random variable with density function
�(�) =
{ �2
4 − � + 1 2 ≤ � ≤ 3
� − 2 − �2
12 3 ≤ � ≤ 6
0 ��ℎ������
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