Study Cards

Note: Click the card to reveal the answer

1/7

Question

What is a Binomial expression?

Answer

A binomial is an algebraic expression that contains two different terms connected by addition or subtraction.

Question

What is factorial?

Answer

Factorial (denoted '!') is the product of an integer and all the integers below it.

Question

What is the binomial distribution formula?

Answer

P(X=k)=(nk)pk(1−p)n−k P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}

Question

How is Pascal's Triangle constructed?

Answer

Pascal's Triangle is constructed by placing a 1 in the first row (row 0). Each subsequent row is calculated by adding the two numbers directly above the number we need to calculate. The outer diagonals will always be 1s.

Question

What conditions need to be satisfied in order to use a binomial distribution?

Answer

- A fixed number of trials
- Indepent trials
- Only two outcomes (success or failure)
- The probability of success remaining unchanged for all trials.

Question

What is the formula for (nk) \binom{n}{k} ?

Answer

n!k!(n−k)! \frac{n!}{k!(n-k)!}

Question

What is the binomial expansion formula?

Answer

(a+b)n=an+(n1)an−1b+(n2)an−2b2+⋯+bn (a+b)^n = a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \dots + b^n