Chapter 10: Q. 10.3 (page 431)

Give an efficient algorithm to simulate the value of a random variable with probability mass function
p1 = .15 p2 = .2 p3 = .35 p4 = .30

Short Answer

Expert verified

The algorithm is define $X$ using the Uniform continuous distribution $U$ over $(0, 1)$ .

Step by step solution

Given Information

We have given the probability mass function

$p_{1} = . 15 p_{2} = . 2 p_{3} = . 35 p_{4} = . 30$

Simplify

Generating $U ~ U n i f (0, 1)$ .

Now, declare $X$ as follows

$X = \{\begin{cases} 1, & U \in (0, 0.15) \\ 2, & U \in (0.15, 0.35) \\ 3, & U \in (0.35, 0.7) \\ 4, & U \in (0.7, 1) \end{cases}$

Consider that because of the construction we have, for example

$P (X - 1) = P (U \in (0, 0.15)) = 0.15 = p_{1}$

and similarly for all other values

$P (X = i) = p_{i}$

So, we have $X$ follows the required discrete distribution.

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Give an efficient algorithm to simulate the value of a random variable with probability mass function
p1 = .15 p2 = .2 p3 = .35 p4 = .30

Short Answer

Step by step solution

Given Information

Simplify

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Give an efficient algorithm to simulate the value of a random variable with probability mass functionp1 = .15 p2 = .2 p3 = .35 p4 = .30

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Discrete Mathematics

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Give an efficient algorithm to simulate the value of a random variable with probability mass function
p1 = .15 p2 = .2 p3 = .35 p4 = .30