Explore BrainMass

# Mixing the Constant with the Normal

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

There is a minor typo in the part(d).
The function should be 1/(b-a), not 1/(a+b).

From Conditional distribution and the Bivariate Normal distribution.
Thank you.

https://brainmass.com/math/probability/mixing-constant-normal-162855

## SOLUTION This solution is FREE courtesy of BrainMass!

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Solution. By (b), we know that for all

,

where c and d are constants.

By (c), we know that

which is a constant independent of t.

Then by a), b) and c), we can write the conditional probability density function as follows.

................(*)

Note 1): (*) shows that the conditional probability distribution is a normal distribution with mean ct+d and standard deviation as stated in (b) and (a).

Note 2): exp(x) denotes the exponential function

By d), we know that the marginal distribution in X is

So, by a formula for the joint p.d.f.: , we can get the joint p.d.f. as follows. For every real number y,

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!