- #1
Eren10
- 17
- 0
Hi,
I want to proof what the distribution will be when I apply a normal distributed x to a linear function y = a*x + b. What will be the mean and the variance of y ?
The expectations can be calculated than with this formula ( probably with this formula what i want can be proofed with substitution):
E_x [y] = integral ( y(x)*rho_x(x)dx) , x is the randomly event , normal distributed, y = a*x+b.
After this I want to proof that for n - dimensional parameter the variance [tex]\sigma = \sum\sigma^2[/tex]
for example I want also proof that the sum of normal distributed parameters X and Y is also normal distributed.
can someone at least advice which book I need to see how this kind of things are proofed.
I want to proof what the distribution will be when I apply a normal distributed x to a linear function y = a*x + b. What will be the mean and the variance of y ?
The expectations can be calculated than with this formula ( probably with this formula what i want can be proofed with substitution):
E_x [y] = integral ( y(x)*rho_x(x)dx) , x is the randomly event , normal distributed, y = a*x+b.
After this I want to proof that for n - dimensional parameter the variance [tex]\sigma = \sum\sigma^2[/tex]
for example I want also proof that the sum of normal distributed parameters X and Y is also normal distributed.
can someone at least advice which book I need to see how this kind of things are proofed.
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