Suppose there are n independent trials of an experiment with k3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?

The formula of an expected count is given by .

Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes,

where pi represents the probability of observing the ith outcome.

The expected counts for each possible outcome are given by .

Where, is the probability of observing the ith outcome

is the expected count of the ith outcome.

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Complete question :

Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes, where Pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?

Ei = nPi

Step-by-step explanation:

Since Pi represents the probability of observing the ith outcome

The number of independent trials n = k>3 :

Expected outcome of each count will be the product of probability of the ith outcome and the number of the corresponding trial.

Hence, Expected count (Ei) = probability of ith count * n

Ei = nPi