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Hello everyone.
00:02
So in this question for given pdf for random variable we have to design the simulation algorithm using inverse transformation method.
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So the pdf given is fx is equals to 1 divided by 2 for x line between 0 2 1, 1 divided by 8 for x line between 1 to 3 and 1 divided by 12 for x line between 3 to 6.
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Now first we find cdf, this is a pdl, that is probability density function.
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Next we find cdl, cumulative density function, which is given as fx.
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It is defined as fx is equal to integration of fx dx, integration over the interval of x.
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So using this we can write cdff x is equals to we integrate 1 divided by 2 for range 0 to 1 which gives x divided by 2 for interval 0 to 1.
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Similarly we integrate 1 divided by 8 for interval 1 to 3 so we get x divided by 8 plus 3 divided by 8 and similarly we get 1 divided by 2 plus x divided by 12.
02:13
Now talking about the algorithm for inverse transformation method, algorithm for inverse transformation method, that is itn, we have step 1 is to generate a random number from uniform distribution...