WEEK 3 Flashcards
Normal distribution
Continuous data above or below a point
need mean and sigma
standardize z = x - mean divide sigma
find table ; left side = below data point
right side = 1-p (from the table)
Bernolli
2 outcomes (dichotomous variables) are mutually exclusive and they add up to 1
male or female, student or not, native or not
we need a proportion of an outcome
1 = p
0= 1-p
its parameterised b p = probability of success
Mean of Bernolli
p gives mean to distribution
X = E(X) = p
variance = VAR (X) = p(1-p)
standard deviation = square root (p(1-p))
its always positive
Binomial distribution
cover n peple or thinks we count how many have happened
just add N bernoullis assuming p are indpenedent
E(X) = n x p
Var (X) = n x p x (1-p)
the n and p
determine the shape of the binomial distribution it is parameterised by them
binomial
n = number of goes
r = number of required’successes’’
p = probability of the results you’re looking for
r successes
n - r
not successes
1- p
each branch has a probability .
p(r) (1-p) (n-r)
p (r success in n goes)
n C (under r) x pr x (1-p) *n-r
if p is higher than 0.5 bulk is on the right
left skewed
A binomial distribution is a discrete probability distribution
a variable can only take on one of the 2 values
p is constant from trial to trial
successive events are independent.
exactly 0.5 skew
symmetric
if p is low (less than 0.5),
The bulk of distrubtion is to the left, leaving a tail on right.
= right skewed
Each outcome is mutually exclusive of the rest
and n gets larger, the mani bit of the distribution gets smoother
Bernolli
p = people with the characteristic / n (all people)
mean varince = find p
then p x (1-p)
Binomial
p (r successes)
C x p *r x (1-p) *n-r
C = n ! / r! (n-r) !
variance in binomial
n x p
distribution
z = x -mean / standard deviation
unstandardise z
x = z x sigma + mean
or sigma = x- mean / z
if p (r >2), if p (r = 0) , if p (r < 1),
1) 1 - ( p (r = 0) + (p (r = 1) + (p (r = 2)
2) 1 x 0.1 *0 x 0.9 *20
3) 20 x 0.1*1 x 0.9 *19
the graph is always symmetric for
normal distribution
e (x) = N
var (x) = sigma squared
N (mean, variance)
( first , 2nd number after 2 )
Loaves of bread have weights that are normally distributed with a mean of 800g and a standard deviation of 3.7g. The heaviest 10% of loaves are sold under a “premium” label. What is the lightest a premium loaf of bread can be?
804.8g
