Specialist Probability
VCE Specialist Mathematics 7/7/2016
Specialist Probability (Topic 4)
This content has been added to the course this year. It has not been covered in any of the last few study designs and is quite different from some of the other topics covered this in Spesh.
Beware that this is highly likely (re. almost certain) to feature on the end of year exam heavier than other topics.
Methods Probability
Specialist
Discrete Random Variables:
‘X’ is a distinct natural number of events occurring (ie. No. of Facebook messages received in a day
Pr(X=x)
As the week progresses (eg.)
0,0,1,1,0,3, etc.
Continuous Variables
A continuous random variable graph takes and plots them on a plane, joined together with a line.
Continuous is the opposite of discrete and therefore rational values are also possible.
The probability of any specific value is really small, but we can use a definite integral to find the probability being contained in a range.
Specific odds are given as:
x * f(x) *dx
To find the value with a given probability, we integrate over – ∞to ∞.
Normal Distribution
This is a special kind of prob. distribution. The highest point on this when graphed is the mean value over the entire sample. From this we can calculate the modal value.
For any value the probability of a value falling between -1 and 1 from the mean, the area between in always about 0.68. With a standard deviation of 3, the probability falls to about 0.997.
As usual, the material covered in specialist maths depends heavily upon (and is similar to) the work in Maths Methods.
µ symbolises the mean value
Σ symbolises the spread.
N denotes the total population