# Thread: Show the limit of a discrete markov chain's distribution converge to a continuous one

2. ## Re: Show the limit of a discrete markov chain's distribution converge to a continuous

How do you get the expression in part b)?

If you are following the hints, you should try to evaluate the CDF of first and take . Although I have not calculate it, the expression you put down here does not like the CDF of a geometric distribution.

3. ## Re: Show the limit of a discrete markov chain's distribution converge to a continuous

One of the main things bothering me is that the denominator inside the brackets is N whilst the exponent is x, the two being different meaning I can't use what I thought i needed to use in my previous post

4. ## Re: Show the limit of a discrete markov chain's distribution converge to a continuous

You have not get the CDF of correctly.

The CDF of is not dividing the CDF of by .

A simple way to transform it is to consider

so now it is in terms of the geometric CDF you just found.

5. ## The Following User Says Thank You to BGM For This Useful Post:

Maharero (10-05-2015)

6. ## Re: Show the limit of a discrete markov chain's distribution converge to a continuous

Thank you for teaching me that, it makes sense. I worked through the problem like before and now was able to reach the CDF of the exponential distribution as I wanted

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