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SMA Week10 - Coggle Diagram
SMA Week10
review of PMF, PDF, CDF
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X = R.V, whereas x is the value of the random variable
note that value of a fixed point for continuous r.v (such as unif) is 0, so P(U = 0.5) = 0
CDF of discrete random variable: P(X <= xk) = P(X = x1) + P(X = x2) + P(X = x3) + ... P(X = xk) = p1 + p2 + p3 + ... pk
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- generating realisations of input random variables
- given a distribution of a random variable X, how do we generate samples of X
what if R commands dont exist to generate random samples of the distribution. we want to transform the unif R.V to generate the samples of X
generate discrete R.V
there can be a finitely large number of samples, n, but each of them have to occur with a given probability (so that is a probability mass function). our task is to generate these samples given we know the probability mass function (i.e. given we know that X = 9 takes the prob 0.07, X = 10 takes the prob 0.15 etc ). starting from a unif random variable, our task is to transform the unif random variable such that we obtain a histogram of samples that correspond to the prob mass function. these samples would be used later on for output analysis
generate continuous R.V
given the CDF of a continuous random variable, how do we generate samples of X
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