# User talk:Swachira

**Welcome to Wiki Course Notes!**
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Again, welcome and have fun! WikiSysop 20:30, 8 May 2013 (MDT)

## Thursday 9th May 2013 Summary

Sampling methods:
1. **Multiplicative Congruential Algorithm**
This is algorithm involves three integer parameters; a, b and m, and an initial value x, known as the seed.
A sequence of numbers is defined by
x_{k+1} = ax_{k} + b mod m
where mod m means take the remainder after division by m.
Therefore the random values are between 0 and m inclusive.
To normalize the values, we divide by m-1, resulting in numbers uniformly distributed in the interval [0, 1].

2.**Inverse Transform Method**
We use this method when we want to see a certain trend in our random values, such as an exponential trend.
The steps involved in this algorithm include:
Step 1:
Take U~U[0,1]

Step 2:
Define X = F^{-1}(U)
Where F(x) = P(X<=x) (the cdf of the distribution we wish to map our random data)

F^{-1}(.) denotes the function inverse of F(.)

Therefore F(X)= P(X<=x)

= P(F^{-1}(U) <= x) = P(F(F^{-1}(U) <= F(x)) = P(U<= F(x))