# Create a conditional distributionΒΆ

In this example we are going to build the distribution of the random vector X conditioned by the random variable Theta

with Theta obtained with the random variable Y through a function f

```from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
```

create the Y distribution

```YDist = ot.Uniform(-1.0, 1.0)
```

create Theta=f(y)

```f = ot.SymbolicFunction(['y'], ['y', '1+y^2'])
```

create the X|Theta distribution

```XgivenThetaDist = ot.Uniform()
```

create the distribution

```XDist = ot.ConditionalDistribution(XgivenThetaDist, YDist, f)
XDist.setDescription(['X|Theta=f(y)'])
XDist
```

ConditionalDistribution(X with X|Theta~Uniform(Theta), Theta=f(Y), f=[y]->[y,1+y^2], Y~Uniform(a = -1, b = 1))

Get a sample

```XDist.getSample(5)
```
X|Theta=f(y) 0.635176 0.4034392 0.3888339 0.9779865 0.4113054

draw PDF

```graph = XDist.drawPDF()
view = viewer.View(graph)
plt.show()
```

Total running time of the script: ( 0 minutes 0.102 seconds)

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