- Descriptive Statistics
- Quantative Analysis of Data
- Distribution of Data
Show that Constants are Normally Distributed
Let X1 and X2 denoted independent, normally distributed random variables, not necessarily the same mean or variance. Show that any constants "a" and "b", Y= aX1 + bX2 is normally distributed.
I'm not sure if I can just prove it by showing what I have below.
SX2 ---> INTEGRATION FROM X_2
SX1 ---> INTEGRATION FROM X_1
E[aX1 + bX2 ] = SX2 SX1 (aX1 + bX2)f(X1, X2) dX1 dX2
= a SX2 SX1 X1 f(X1, X2) dX1 dX2
+ b SX1 SX2 X2 f(X1,X2) dX1 dX2
= aE[X1] + bE[X2 ]
and then do Variance as well.