I am trying to figure out the probability distribution for weekdays with the issue that the days have not been sampled evenly.
For a study, respondents where asked to fill a questionnaire during one weekday and one weekend. Each respondents then have filled 2 questionnaires, one during a weekday and the other during the weekend.
My guess is that the probabilities are then 1/5 for weekdays and 1/2 for weekend days. Is this right ?
Which distribution I am supposed to use to approximate the probabilities of finding one particular day ? Can I use a binomial one ? How should I take into account the different probabilities ?
If I want for example the probability of getting a Monday using the binomial dist. can I do something like this :
$$ P(1\text{ Monday }) = P(X = 1) $$
$$ = {7\choose 1} (\frac{1}5 \times \frac{1}2) ^1 (1-\frac{1}5 \times \frac{1}2)^{7-1}$$
How I am supposed to approach this problem ?
I am not sure how to deal with the unequal probabilities.
Any ideas ? Thanks.