How Do I Complete the Square and Simplify This Equation?

[gerv13]

Hi, I'm almost at the end of a question but i seem to be stuck. I have the answer though.. so I am up to here so can someone please help me complete this:

$$(\frac{n + \frac{1}{c}}{\frac{s}{n} }) [\mu^2 - 2\mu(\frac{n \overline{y}}{n+\frac{1}{c}})]$$
then i completed the square:
$$(\frac{n + \frac{1}{c}}{\frac{s}{n} }) [(\mu - \frac{n\overline{y}}{n + \frac{1}{c}})^2 - (\frac{n\overline{y}}{n + \frac{1}{c}})^2]$$

then i expanded it:
$$(\frac{n + \frac{1}{c}}{\frac{s}{n} })(\mu - \frac{n\overline{y}}{n + \frac{1}{c}})^2 - (\frac{n + \frac{1}{c}}{\frac{s}{n} })(\frac{n\overline{y}}{n + \frac{1}{c}})^2$$

then i guess:
$$(\frac{n + \frac{1}{c}}{\frac{s}{n} })(\mu - \frac{n\overline{y}}{n + \frac{1}{c}})^2 -$$$$(\frac{n + \frac{1}{c}}{\frac{s}{n} })(\frac{1}{(\frac{n\overline{y}}{n + \frac{1}{c}})^2 })$$

and then i tried really hard to simplify it but i can't get the answer...

then answer is:
$$\frac{n + \frac{1}{c}}{\frac{s}{n} + \frac{\overline{y}(\frac{1}{c})}{(n + \frac{1}{c})}}[\mu - (\frac{n\overline{y}}{n + \frac{1}{c}})]^2$$

am i doing it right so far? and if so, then can you please help me figure out the next line, coz i tried and i can't somehow get that answer..:(.. thank you..?

 

[mathman]

What is the statement of the original problem?

 

[arildno]

Do you have some equations relating some of the variables together, so that they are not fully independent of each other?

Otherwise, I don't think you will make it.

Please post the precise question, so that we can look at it from there!

 

[gerv13]

yeahh i think that i must have done something wrong along the way, coz i don't think that i could make it too..

well the actual problem was to show:
$$p(t|y) \propto (1 + \frac{n + 1/c}{\frac{s}{n} + \frac{\overline{y^2}(1/c)}{n + 1/c}})(\mu - \frac{n\overline{y}}{n + 1/c})^2$$

but yeahhh what i showed you guys is where I am up to which is sort of 3/4 of the way done i think. but yeahh i started again after reading all your posts, so do you think that it's possible to get from
$$(\frac{n + 1/c}{\frac{s}{n}})[\mu - \frac{n\overline{y}}{n + 1/c}]^2$$

and make it equal to
$$\frac{n + \frac{1}{c}}{\frac{s}{n} + \frac{\overline{y}(\frac{1}{c})}{(n + \frac{1}{c})}}[\mu - (\frac{n\overline{y}}{n + \frac{1}{c}})]^2$$

like i tried
$$\frac{n + \frac{1}{c}}{\frac{s}{n} + \frac{\overline{y}(\frac{1}{c})}{(n + \frac{1}{c})}}[\mu - (\frac{n\overline{y}}{n + \frac{1}{c}})][\mu - (\frac{n\overline{y}}{n + \frac{1}{c}})]$$

and expanding out only the first two brackets and that didn't work out too..
so did i do something wrong again and it's not possible to get to the right answer with what I am up to so far? and should i start again?

 

[mathman]

You need to define p(t|y).