Chapter 3.2 Exercise 1

Compute the following:

(a)\({6 \choose 3}\) = 20

choose(6,3)
## [1] 20

\({n \choose j}=(n)_j/j!=n!/j!(n-j)!\) = 6!/3!(6-3)!= 20

factorial(6)/(factorial(3)*factorial(6-3))
## [1] 20
  1. \(b(5, .2, 4)\) =

\(b(n, p, j) = {n \choose j}p^jq^nāˆ’j\) where \(q = (1-p)\)

= \({5 \choose 4}(1/5)^4*(4/5)^1\)

choose(5,4)*(1/5)**4*(4/5)
## [1] 0.0064

(c)\({7 \choose 2}\) = 35

(d)\({26 \choose 26}\) = 1

  1. \(b(4, .2, 3)\)
choose(4,3)*(1/5)**3*(4/5)
## [1] 0.0256

(f)\({6 \choose 2}\) = 15

(g)\({10 \choose 9}\) = 10

  1. \(b(8,.3,5)\)
choose(8,5)*(.3)**5*(.7)**3
## [1] 0.04667544