sample and population mean

I am OK with the sample mean and variance

But for the population mean, everywhere I looked it is a "confidence interval" based on the sample mean and standard error (which I understand), and never seen a "point estimate" as in the pic (eq 2.5).

So could anyone please find me a link where this topic is discussed?

Wikipedia is always my go-to for stuff like this...

http://en.wikipedia.org/wiki/Point_estimate

Sorry I have tried but still couldn't find anything that resemble that formula, or anything about an estimate of the population mean actually.

If you have a direct link to the page please post it.

To give more detail, the excerpt is from a finance course about the Black–Scholes formula, and the more I checked it seems to be more about Geometric Brownian motion.

So is that formula specifically for Geometric Brownian motion, and not statistic in general?

Not sure about the relevance to finance. If X(t) is a brownian motion with mean µ Delta t and variance sigma^2 Delta t, then Y(t) = exp X(t) would have a mean of exp( µ Delta t - sigma^2/2 Delta t), if I remember correctly.....

Quote: andysif

To give more detail, the excerpt is from a finance course about the Black–Scholes formula, and the more I checked it seems to be more about Geometric Brownian motion.

So is that formula specifically for Geometric Brownian motion, and not statistic in general?

Yes, as is noticeable from the Δt element.

In general, there is no special time relationship; a sample is often a one-time picture of a situation. Or, you have a chronological series, but where time is not an explanator, just an index.

Sample mean (or average) is the result of a random draw (this specific sample),
Population mean is the theoretical constant parametre describing the subjacent population / phenomenon.
Sample mean is the point estimator of population mean.
Confidence interval is when you want to add an error buffer around the point estimator.

Quote: kubikulann

Yes, as is noticeable from the £Gt element.

In general, there is no special time relationship; a sample is often a one-time picture of a situation. Or, you have a chronological series, but where time is not an explanator, just an index.

Sample mean (or average) is the result of a random draw (this specific sample),
Population mean is the theoretical constant parametre describing the subjacent population / phenomenon.
Sample mean is the point estimator of population mean.
Confidence interval is when you want to add an error buffer around the point estimator.

Thank you very much

>Sample mean (or average) is the result of a random draw (this specific sample),
... such as the temperature measures that you made during a month
>Population mean is the theoretical constant parametre describing the subjacent population / phenomenon.
....The actual average temperature during that month
>Sample mean is the point estimator of population mean.
>Confidence interval is when you want to add an error buffer around the point estimator.
...Such as how good your particular point estimate is to the point estimates of others who sampled the same phenomenon, such as the temperature of that particular month but used different equipment or techniques.

Thanks.

The point I am confused is I have never seen that equation relating the sample mean and population mean:

U-bar = miu - ((sigma^2)/2) * delta t