Update beta_binom_post_plot.py

[patel-zeel]

Description

Updated the code that generates figure 4.10 to avoid the confusion between likelihood and prior/posterior range.

Figure Number

book1 - 4.10

Figures

gist

Issue

#683

Steps

• Updated the code following the PEP 8 guidelines.
• Replaced numpy with jax.numpy following the CONTRIBUTING.md guidelines.
• Using exp -> sum -> logpmf instead of prod -> pmf to avoid numerical underflow.

Checklist:

• Performed a self-review of the code
• Tested on Google Colab.

Potential problems/Important remarks

I have modified the colors and line styles to make plots visually separable when they superimpose. Please let me know if this is violating rules for using specific colors and styles for likelihood, prior and posterior.