Write code in Python(jupiter)

Given X1,,XniidP(), one wants to define a conjugate prior for . 1 1. Write the Poisson distribution as an exponential family. 2. Find the conjugate prior relying on the presentation as an exponential family. 3. Check that the prior you found is a Gamma distribution (,), defined by the following density function: (,)=()1e, with ,>0. The Gamma function is defined by (z)=0tz1etdt, for any complex number z with (z)>0. 4. Let X=(X1,,Xn). Write the posterior distribution of as a function of X and the hyper parameters