MATH268: Assignment 4
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MATH268: Assignment 4
Exercise 1 Use the rejection method to simulate a random variable with the p . d.f. given by f (t) = 30(t2 - 2t3 + t4 ), 0 < t < 1,
and f (t) = 0 otherwise.
[25 marks]
Exercise 2 Let U1 , U2 , . . . be a sequence of i.i. d. U (0, 1) random variables. Let N be such that N + 1 = min{m e {1, 2, . . . } : ΠUi < e −入 }. Verify that N follows the Poisson distribution with parameter λ . (One may do this by relating to a suitable Poisson process.) Use this result to formulate a method for simulating Poisson(λ).
[25 marks]
Exercise 3 Consider a random variable with the p . d.f. given by
f (x) = (1 - x2 ), - 1 < x < 1
and 0 otherwise. Simulate the variable by using the rejection method.
[25 marks]
Exercise 4 Explain in detail how to use the inverse function method to simulate a random variable with a logistic distribution p . d.f.
e −z
f (x) =
.
[25 marks]
2022-12-03