Binomials

Question 1

Find the first 3 terms in ascendind powers of x,of the binomial expansion of (2 - x/2)^7,giving each term in its simplest form.

Answer 1

Step 1: know your a, b and n values are
“a = 2 b = -x/2 n = 7”

Step 2: Substitute the a, b and n values onto the binomial formula
•(a + b)^n = a^n + (n^C1) a^n-1 b + (n^C2) a^n-2 b^2 + … + (n^Cn-1) ab^n-1 + b^n

“(2 +- x/2)^7 = 2^7 + (7^C1) 2^7-1 -x/2 + (7^C2) 2^7-2 - x/2^2 + … + (7^C7-1) 2- x/2^7-1 + -x/2^7”

Answer: , 128- 224x +168x^2

Question 2

Assumptions for binomial distributions

Answer 2

1) fixed number of trials
2) probability of success is constant
3) each trial is independent
4) each trial is either success or failure

Question 3

Factorial Notation

Answer 3

You can use factorial notation and your calculator to find entries on pascal’s triangle quickly.

the number of ways of choosing r items froma group of n items fom a group can be written as nCr or n over r

Question 4

Binomial estimation

Answer 4

if the value for x is less than 1 then x^n gets smaller as n gets larger
if x is small you can sometimes ignore large powers of x to approximate a function or estimate a value