Binomial distribution Flashcards
1
Q
What does the notation n! mean?
A
n(n-1)(n-2)…1
2
Q
How many ways can n objects be arranged?
A
n!
3
Q
What does the notation ⁿCₐ mean?
A
n!/(a!(n-a)!)
4
Q
How many ways can n objects be arranged when there’s a of one type and n-a of another?
A
ⁿCₐ
5
Q
How is a binomially distributed variable notated?
A
X∼B(n,p), where n is the number of trials and p is the probability of each trial being a success
6
Q
What conditions are required for a binomial distribution?
A
- A fixed number of trials
- Each trial can only result in a success or a failure
- The trials are independent
- The probability of success is constant for each trial
7
Q
For a random variable X∼B(n,p), how can P(X=x) be calculated?
A
ⁿCₓpˣ(1-p)ⁿ⁻ˣ
8
Q
For a random variable X∼B(n,p), how can E(X) be calculated?
A
np
9
Q
For a random variable X∼B(n,p), how can Var(X) be calculated?
A
np(1-p)
