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# A challenge!

Let's do a multinomial experiment i.e. there are $$m$$ no. of possibilities on each trial and we do $$n$$ number of trials.

Moreover, the probability of getting a particular possibility at $$i$$th trial also varies, each differently, like $$a_k(i), 1 \le k \le m$$

What is the expected number of times of getting a particular possibility (let's say the one with index 1)?

Note by Kartik Sharma
6 months, 1 week ago

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The answer is $$\displaystyle \sum_{i=1}^n {a_k(i)}$$ for the $$k$$th possibility. · 6 months, 1 week ago