# The CDF of an i.i.d. sample realizations

Is it possible to draw the CDF of the empirical measure $\hat{P}_x$ for a i.i.d. sample realizations where $X_1 = 0.3$,$X_2 = 5$,$X_3 = 1.5$, $X_4 = 3.4$ without knowing the distribution?

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@did do we assume that each value has a 25% probability of occurence? thanks –  ChuckM Oct 2 '12 at 6:31
Wikipedia gives 10 different ways of estimating the quantiles –  Henry Oct 2 '12 at 7:36
ok I now I see what should be the correct way –  ChuckM Oct 2 '12 at 8:08
thanks @did. how can I approve your answer? –  ChuckM Oct 2 '12 at 19:16

## 1 Answer

Yes: the empirical CDF depends only on the sample (this is what empirical refers to), here the set of values 0.3, 5, 1.5, 3.4. Even the order in which these values appeared is lost in the empirical CDF.

do we assume that each value has a 25% probability of occurence?

The empirical distribution puts mass k/n on each value, where k is the number of times said value appeared in the sample of size n. In your case, n=4 and the values are all different hence yes, each gets a weight 1/4.

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