C'R'V Continuous Random Variable

1
C.R.V (Continuous Random Variable)
The normal curve is a CRV. Where the variable z
can take any value and the probabilities can be
worked out. Information does not always give a
normal curve, sometimes it gives other curves or
a straight line, or a combination.
The bit that confuses everyone! f(x) is the
equation of the line or PDF(probability density
function) F(x) is the area under the curve or
CDF(cumulative frequency function) If you
integrate f(x) dx you get F(x) If you
differentiate F(x) dx you get f(x)
2
The number of trains that are late are recorded
in a histogram.
The histogram can be modelled by this line for
which we can find a function
Frequency Density
0 2 4 6 8 10 Minutes late
Note that the area under this curve is 1(we will
come back to this later)
3
A CRV X has PDF
for
1) Sketch the graph of f(x) 2) Show that the area
under the curve is 1 3) Find P(Xlt2) 4) Find
P(1.5ltXlt2.6
4
A CRV has a PDF
1) Find k 2) Sketch f(x) 3) Find P(1ltXlt3) 4)
Find P(Xgt2)
5
P231