Download Maths Methods - Outcome 6 - Probability

Mathematical Methods
Outcome 6- Probability
T wo -state Ma rko v C ha ins: the result of each trial is
conditional on the result of the previous trial
C ontinuous prob abil ity: it can take any value
in a given interval
The general structure of a transition matrix:
S te ady state o f a Marko v chain:
The properties of the probability density function:
1. f(x)≥0 for all x
!
2. ∫!! 𝑓(𝑥)𝑑𝑥 = 1
Geo metric Dis trib utio n:
It is different to binomial and markov chain.
Typically a question will ask:
e.g. What is the probability that you have x failures before
success:
Tip:
1. f(x) does not have to be smooth curve. They
can be other shapes too!
Ex pected value o f a c ontinuous prob abili ty
dens ity func tio n:
N ormal Di stri bution: it may take any value within a
given range, and no distinct, countable values.
Variance
It has the following properties:
1. Symmetrical
2. Bell shaped
3. Mean=mode=median
S ta nd ard isa ti on and the 6 8-9 5-9 9.7 % rule
P erce ntile and the media n
The median for continuous random variable is such
that:
99.7% of the values
lie within three
standard deviation
of the means
We can solve this on the calculator (CAS):
95% of the values
lie within two
standard deviation
of the mean
The interquartile range of X is:
IQR= b-a
68% of the values
lie within one
standard deviation
of the mean
Calculator tips:
We can determine normal probabilities using this
To standardise, we use Z=
!!!
!