Monthly Archives: November 2016

DSL for Generative Models (51/365)

The backlog becomes longer. I’ve changed jobs two weeks ago and it has upset my routine. No matter. Here we go again. I want to deviate from my problem solving mode for a while and use up a few posts … Continue reading

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Random Variables – Problem (50/365)

Moving on to the next chapter “Random Variables – I”, take a look at the following problem. Show that the random variable is continuous if and only if for all . (Forward direction) Suppose is a continuous random variable, then … Continue reading

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Measurable Spaces – Problem (49/365)

Let be the Lebesque-Stieltjes measure generated by a continuous function. Show that if the set is at most countable, then . A Lebesque-Stieltjes measure is a countably additive measure and is given by a generalized distribution function such that that … Continue reading

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Measurable Spaces – Problem (48/365)

Another question on distribution functions. Show that each of the functions is continuous on the right but is not a distribution function in . Take the first function. To show that it is continuous on the right, let and let … Continue reading

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Measurable Spaces – Problem (47/365)

The previous post involved distribution functions over the real numbers but it’s also possible to have distribution functions over . A problem asks to show that if we have the distribution function And a difference function Then show that Just … Continue reading

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