# Create a Bayes distributionΒΆ

In this example we are going to build the distribution of the random vector

with X conditioned by the random variable Theta obtained with the random variable Y through a function f

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

ot.Log.Show(ot.Log.NONE)
```

create the Y distribution

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

create Theta=f(y)

```f = ot.SymbolicFunction(["y"], ["y", "1 + y"])
```

create the X|Theta distribution

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

create the distribution

```XDist = ot.BayesDistribution(XgivenThetaDist, YDist, f)
XDist.setDescription(["X|Theta=f(y)", "y"])
XDist
```
BayesDistribution
• name=BayesDistribution
• dimension=2
• weight=1
• range=[-1, 1] [-0.999956, 1.99996]
• description=[X|Theta=f(y),y]
• isParallel=false
• isCopula=false

Get a sample

```sample = XDist.getSample(100)
```

draw PDF

```graph = XDist.drawPDF()
cloud = ot.Cloud(sample)
cloud.setColor("red")
cloud.setLegend("sample")