I have basic question regarding probability distribution mathematical expressions. I need to design a model who should calculate probability of choosing seat number in the cinema theater by people and it is told that this follows exponential distribution.

Also given that this probability is also multiplied by some factor $\sum_{i=1}^k AB_i$ . Now considering N number of seats from 1 to N. I could easily get probability of particular seat selection as $Pu=1/N$ for any one of the seat, being same, if i were using uniform distribution. So the expression for probability would be $P = Pu $ $\sum_{i=1}^k AB_i$ or

$P = \frac{1}{N} $ $\sum_{i=1}^k AB_i$

But i have to use exponential distribution for seat selection instead of uniform distribution, so how i can get this seat selection probability $Pexp$. i.e

$P= Pexp * \sum_{i=1}^k AB_i$

what would be in place of $Pexp$?

  • $\begingroup$ I was going to type your mathematics correctly for you, but i don't understand you. If you do this, its more likely that someone will vote to reopen. You can find a short tutorial here math.meta.stackexchange.com/questions/5020/… , you want to do things like $\sum_{i=1}^\infty AB_i$ for $\sum_{i=1}^\infty AB_i$. $\endgroup$ Jan 9, 2020 at 5:41
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    $\begingroup$ Thanks calvin, i have modified equations. $\endgroup$ Jan 9, 2020 at 8:02
  • $\begingroup$ It looks much better. Can you also explain a little what $A$ and $B_i$ are? $\endgroup$ Jan 9, 2020 at 8:06
  • $\begingroup$ About $AB_i$ i just know that these are conditional probabilities calculated earlier. $\endgroup$ Jan 9, 2020 at 8:36