Binomial Distribution

Question 1

First, how to tell if it’s a binomial distribution?

Answer 1

• 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)

Question 2

P(X = 7) what do?

Answer 2

• Binomial PD

Question 3

How to know if its =?

Answer 3

When it says “exactly”

Question 4

P(X ≤ 5) what do?

Answer 4

• Binomial CD

Question 5

How to know if its ≤?
(less than or equal to)

Answer 5

e.g.
“no more than 8 mistakes”
“3 or fewer faulty components”

Question 6

P(X < 3) what do?

Answer 6

• Binomial CD
• minus 1 so, u do Binomial CD: P(X < 2 )

Question 7

How to know if its <?

Answer 7

“less than” pretty much?
“fewer than 5 mistakes”

Question 8

P(X ≥ 9) what do?

Answer 8

• Binomial CD
• minus 1 so, u do Binomial CD: P(X < 9)
• 1 minus ans = yaa

Question 9

How to know if its ≥?

Answer 9

“at least”??

Question 10

P(X > 6) what do?

Answer 10

• Binomial CD
• 1 minus ans = yaa

Question 11

How to know if its >?

Answer 11

“more than”
ig it’s kinda logical

Question 12

P(4 < X < 9) what do?

Answer 12

• 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)

Question 13

How to know if its ° < X < ° ?

Answer 13

It’ll say it’s inclusive

Question 14

However what u do if it’s not inclusive?

Answer 14

U don’t minus any of them?
Just do per usual, it’s still less than or equal to

Question 15

How to do inverse aka how to find n?

Answer 15

its (log e answer) divided by (log e probability)

Question 16

How to know if it’s poisson distribution?

Answer 16

• Events occur independently
• At random
• At a constant average rate

X ~ Po (λ)

Question 17

Example of a poisson distribution?

Answer 17

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

Question 18

Formula for poisson PD?

Answer 18

(e^-p) x (p^n) ALL DIVIDED BY n!

(that exclamation mark much needed)

Question 19

Poisson way for answering technically the same as binomials,
I’ll show u now

Answer 19

• 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

Question 20

There could possibly be a lil bit more here for this topic that probably does need to be stated sooo ye…. what is it?

Answer 20

4.3 The discrete uniform distribution as a model

no idea what the heck that is

Question 21

How to find n for a binomial distribution if given an answer and the probability?

Answer 21

log_eanswer/log_eprobability = n

Question 22

How to find t for a poisson distribution where it don’t know its length? (u get the answer as well)

Answer 22

In answer/-probability = t

Obscure but if u know, u know
(just look back D:)