#!/usr/bin/env python3
""" LPC stats HW2, Problem 1
    Author: Caleb Fangmeier
    Created: Sep. 25, 2017
"""
from numpy import sum, sqrt
from numpy.random import exponential, poisson


def find_relative_frequency(n_experiments, b):
    # First get the mean counts for each experiment
    mean_counts = exponential(scale=b, size=n_experiments)

    # Since this is a counting experiment, sample from a Poisson distribution with the
    # previously generated means.
    single_counts = poisson(lam=mean_counts)

    # Generate the per-experiment bounds based on the observed single_counts
    bound_low = single_counts - sqrt(single_counts)
    bound_high = single_counts + sqrt(single_counts)

    # Finally, count for how many experiments the mean_count lies in the range
    # calculated above.
    n_pass = sum((bound_low < mean_counts) & (mean_counts < bound_high))
    relative_frequency = n_pass / n_experiments

    # and print the results
    print(f"For b={b}, {n_pass}/{n_experiments} passed, R={relative_frequency*100:4.2f}%")


find_relative_frequency(10000, 5)
find_relative_frequency(10000, 10)