AS/A2
Stats 1
Stats 2
S3
Topic 1:
Combinations of random variables
Graphing aX+bY
The graphs of two Normal distributions are shown:
X~N(100,225) in blue
and
Y~N(80,256) in red
. Shown in black is the distribution of aX+bY. Vary the values of a and b and see what effect they have on the combined graph.
Summary
If X ~ N(
m
1
,
s
1
2
) and Y ~ N(
m
2
,
s
2
2
) then:
aX+bY ~ N(a
m
1
+b
m
2
,a
2
s
1
2
+b
2
s
2
2
)
Based on free Java applets from
JavaMath
Based on
free Java applets from