Binomial Distribution Flashcards
First, how to tell if it’s a binomial distribution?
- A fixed number of trials
- 2 possible outcomes only at each trial
- Fixed probability of success
- Trials are independent of each other
X ~ B (n, p)
P(X = 7) what do?
- Binomial PD
How to know if its =?
When it says “exactly”
P(X ≤ 5) what do?
- Binomial CD
How to know if its ≤?
(less than or equal to)
e.g.
“no more than 8 mistakes”
“3 or fewer faulty components”
P(X < 3) what do?
- Binomial CD
- minus 1 so, u do Binomial CD: P(X < 2 )
How to know if its <?
“less than” pretty much?
“fewer than 5 mistakes”
P(X ≥ 9) what do?
- Binomial CD
- minus 1 so, u do Binomial CD: P(X < 9)
- 1 minus ans = yaa
How to know if its ≥?
“at least”??
P(X > 6) what do?
- Binomial CD
- 1 minus ans = yaa
How to know if its >?
“more than”
ig it’s kinda logical
P(4 < X < 9) what do?
- Binomial CD
- P(X ≤ 9) - P(X < 4)
- Notice on 4 it’s less than, therefore u minus 4 by 1 to do so
Technically it’s
P(X ≤ 9) - P(X ≤ 3)
How to know if its ° < X < ° ?
It’ll say it’s inclusive
However what u do if it’s not inclusive?
U don’t minus any of them?
Just do per usual, it’s still less than or equal to
How to do inverse aka how to find n?
its (log e answer) divided by (log e probability)
How to know if it’s poisson distribution?
- Events occur independently
- At random
- At a constant average rate
X ~ Po (λ)
Example of a poisson distribution?
Calls arrive at a switchboard independently at random at an average rate of 1.4 per minute. Find the probability that:
(a) more than two calls will arrive in a particular minute
(b) more than 10 calls will arrive in a 5-minute interval
(c) between five and nine calls, inclusive, will arrive in a 5-minute interval
(d) more than 20 calls will arrive in a 10-minute interval
(e) 10 or fewer calls will arrive in a 10-minute interval
X ~ Po (1.4)
a - X greater than 2
b - 1.4 x 7, new avg rate, X greater than 10
c - Inclusive soooo, (X ≤ 9) - (X ≤ 4)
d - 1.4 x 10, new avg rate, X greater than 20
e - X less than or equal to 10
Formula for poisson PD?
(e^-p) x (p^n) ALL DIVIDED BY n!
(that exclamation mark much needed)
Poisson way for answering technically the same as binomials,
I’ll show u now
- Poisson pd for P(X = x)
- Poisson cd for P(X ≤ x)
^ and everything else like inclusive, less than, greater than or equal to, greater than, not inclusive, and ya
There could possibly be a lil bit more here for this topic that probably does need to be stated sooo ye…. what is it?
4.3 The discrete uniform distribution as a model
no idea what the heck that is
How to find n for a binomial distribution if given an answer and the probability?
logeanswer/logeprobability = n
How to find t for a poisson distribution where it don’t know its length? (u get the answer as well)
In answer/-probability = t
Obscure but if u know, u know
(just look back D:)
