Binomial Expansion and Distribution

Question 1

Binomial expansion

Answer 1

Expanding (a+b)^2
–> Power of a decreases (first in brackets)
–> Power of b increases (second in brackets)

Question 2

Factorial

Answer 2

Rule = n! = n(n-1)!
eg. 5! = 5x4x3x2x1
(shift x^-1 button on calc. for long factorials (x!))

Question 3

Proof that 0! = 1!

Answer 3

n! = n(n-1)!
1! = 1(1-1)!
1! = 1(0)!
1! = 0! (0! = 1, 1! = 1)
1 = 0

Question 4

Factorials and pascals triangle

Answer 4

nCr = n! / r! (n-r)!

Question 5

Calculator (distribution)

Answer 5

-Menu 7
-Binomial PD for P(X=?)
-Binomial CD for P(X≤?)

Question 6

Binomial distribution (long hand of calc. PD)

Answer 6

P(X=r) =
nCr x p^r x (1-p)^(n-r)

Question 7

Expectation

Answer 7

E(X) =
n x p

Question 8

Accept or reject H0

Answer 8

P > %SL –> Do not reject H0
P < %SL –> Reject H0