ผลต่างระหว่างรุ่นของ "Week11 practice 2"

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We can compute:
 
We can compute:
  
<math>E[\bar{X}]= E\left[\frac{1}{n}\sum_{i=1}^n X_i\right] = \frac{1}{n}
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<math>E[\bar{X}]= E\left[\frac{1}{n}\sum_{i=1}^n X_i\right] = \frac{1}{n}E\left[\sum_{i=1}^n X_i\right] = \frac{1}{n}\sum_{i=1}^n E[X_i] = \frac{1}{n} n\mu = \mu</math>
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=== Sample variances and sample standard deviations ===
 
=== Sample variances and sample standard deviations ===

รุ่นแก้ไขเมื่อ 01:36, 6 พฤศจิกายน 2557

Sample

Consider a certain distribution. The mean of the distribution is the expected value of a random variable sample from the distribution. I.e.,

.

Also recall that the variance of the distribution is

.

And finally, the standard deviation is .

Suppose that you take samples independently from this distribution. (Note that are random variables.

Sample means

The statistic

is called a sample mean.

We can compute:


Sample variances and sample standard deviations