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# Box-Muller Transformation

Unsolved###### Prob. and Stats

##### Problem reported in interviews at

The Box-Muller Rransform is a method for generating normally distributed random numbers from uniformly distributed random numbers. The Box-Muller Transformation can be summarized as follows.

Suppose *u _{1}* and

*u*are independent random variables that are uniformly distributed between 0 and 1 and let:

_{2}\(z_1 = \sqrt {-2 log(u_1)} {cos (2\pi u_2)} \)

\(z_2 = \sqrt {-2 log(u_1)} {sin (2\pi u_2)} \)

Then, z1 and z2 are independent random variables with a standard normal distribution.

Write a function transform(u1,u2) such that when given two uniformly distributed independent random variables (integers), it generates a tuple containing z1 and z2 with standard normal distribution using Box-Muller Transform.

##### Sample Input:

`u1: 0.66971127`

<class 'float'>

`u2: 0.50960964`

##### Expected Output:

`(-0.8938107248822067, -0.05403320867504681)`

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Input Test Case

Please enter only one test case at a timenumpy has been already imported as np (import numpy as np)