T-Distribution

CFA Level I Quant
#1

Hi All,

I have a question on the definition of T-distribution. It is a bell-shaped, centered at its mean probability distributions of sample means. But it is also centered to zero. Does this imply that the mean of sample means is zero??? Why??

Can anyone help me to understand? Thanks in advance!

Thanks,

Sophie

#2

It is similar to the standardized normal distribution. In a standardized distribution, we make mean equal to zero and standard deviation equal to 1. So, when we say it is centered to zero, it simply means that the mean lies at the center. The mean of sample means can have any value.

#3

If the distribution has a true mean of zero, then the sampling distribution of x-bar (an unbiased estimator) will also be zero.

#4

Yes, of course.

#5

Indubitably. I added it because your statement was that the mean of sample means could be any value, where as the original question was about a distribution already centered at zero (and then what the mean of sample means would be). I thought it would be more direct to the original question if we outright confirmed that the mean of sample means (unbiased estimator) is zero because the true mean is zero.

#6

Yes, I missed that part. I thought that OP was talking about T-distribution in general. If the population mean is centered to zero then the mean of sample means should also be zero if it is an unbiased estimator.