You may NOT use any Python packages other than random, math and copy Use your pseudorandom number generator to generate a list of 1000 uniformly-distributed, random,  floating-point numbers between 0 and 1 (duplicates are okay).  Consider these values to represent probability levels pi that can be found by integrating the Gaussian probability density function (PDF) between     x=μ-5⋅σ to x=xi such that pi=P(x

1. You may NOT use any Python packages other than random, math and copy Use your pseudorandom number generator to generate a list of 1000 uniformly-distributed, random,  floating-point numbers between 0 and 1 (duplicates are okay).  Consider these values to represent probability levels p_i that can be found by integrating the Gaussian probability density function (PDF) between 

   x=μ-5⋅σ to x=x_i such that p_i=P(x<x_i|N(μ,σ)) where μ=175, σ=15.

1. Using your Simpson function (nPoints=50) to integrate the Gaussian PDF combined with your Secant method for root finding, find the set of x values compatible with your list of 1000 probabilities.  Note:  you will need to use callback functions for this process.

1. Finally, calculate the estimates of the population parameters μ and σ² using the unbiased sample estimators from your set of x values.  Compare your values to those from N(175, 15).

Output the values for your population estimators like:

Population mean estimate = y.yy

Population variance estimate = z.zz

Note: you may need to use a clamp function to confine your probabilities to fall within the lower limit associated with the lower limit for integration. 

(i.e., make sure p_i≥P(x≤μ-5⋅σ|N(μ,σ))=Simpson(GPDF, (μ, σ), μ-10*σ, μ-5*σ))