Discussion 8

IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

I will be attempting the below:

Exercise 3.

Let X1 and X2 be independent random variables with common distribution Px = 0 (1/8), 1 (3/8), 2 (1/2). Find the distribution of the sum X1 + X2.

Solution:

Let z = X1 + X2

P(z = 0)

P0 <- 1/8*1/8 
P0

## [1] 0.015625

P(z = 1)

P1 <- 1/8*3/8 + 3/8*1/8 
P1

## [1] 0.09375

P(z = 2)

P2 <- 1/8*1/2 + 3/8*3/8 + 1/2*1/8 
P2

## [1] 0.265625

P(z = 3)

P3 <- 3/8*1/2 + 1/2*3/8
P3

## [1] 0.375

P(z = 4)

P4 <- 1/2*1/2
P4

## [1] 0.25

print(c(P0, P1 ,P2 ,P3 ,P4))

## [1] 0.015625 0.093750 0.265625 0.375000 0.250000