<p>Suppose <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as 
<span class="math-container">$$F_X(z)=F_Y(z),$$</span>
where <span class="math-container">$F_X(\cdot)$</span> and <span class="math-container">$F_Y(\cdot)$</span> are the marginal cdfs of <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>, respectively. The 'independently distributed' part means the joint cdf of <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>, denoted <span class="math-container">$F_{XY}(x,y)$</span> is simply the product of the marginal cdfs <span class="math-container">$F_X(x)$</span> and <span class="math-container">$F_Y(y)$</span>, i.e. 
<span class="math-container">$$F_{XY}(x,y)=F_X(x)F_Y(y).$$</span></p>

CC BY-SA 4.0
2019-03-16T04:22:03.513Z
2019-03-16T04:22:03.513Z
dlnB
<p>What does it mean for two random variables to be "identically distributed"? Does it mean that they come from the same probability distribution?</p>

<econometrics><statistics>
Independently and Identically distributed random variables
Martin 
# Independently and Identically distributed random variables

(Asked by: username_0 on 2019-03-16)

What does it mean for two random variables to be "identically distributed"? Does it mean that they come from the same probability distribution?

**Tags:** econometrics, statistics

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## 1 answers

### Answer by username_1 on 2019-03-16. Score: 4 | Accepted answer

Suppose $X$ and $Y$ are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as
$$F\_X(z)=F\_Y(z),$$
where $F\_X(\cdot)$ and $F\_Y(\cdot)$ are the marginal cdfs of $X$ and $Y$, respectively. The 'independently distributed' part means the joint cdf of $X$ and $Y$, denoted $F\_{XY}(x,y)$ is simply the product of the marginal cdfs $F\_X(x)$ and $F\_Y(y)$, i.e.
$$F\_{XY}(x,y)=F\_X(x)F\_Y(y).$$


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