tuesday with me

One cannot imagine how many dinners I have scheduled for today - 3. It is either everyone wants to spend Tuesday with me or everyone in my universe is free on Tuesday. So let's see how did it happened?

Bored as I am now, I model this as a stochastic processes. We can use it to calculate the probability of social dinner clashing on the same day. Let's see how this goes. [Disclaimer: This is done in the name of fun. Appreciate my typing out of the equations and not try to rigorously examine the substance of it.]First, I think its reasonable to assume that the probability of being called for dinner follows a Non Homogeneous Poisson Processs.
Lambda is the rate parameter which is a function of time. Let's use an increasing exponential function to model it, since I tend to get called out for dinner more often over the weekends.
To be more precise, we should actually account for festivities and exams. But for simplicity, let's assume each week is the same (i.e. I get the same number of calls for dinner during exam and during X'mas). Solving, probability of being called for Tuesday should be something like that:-
Now that I have arrived here, I do not see any purpose of doing all these. To get reasonable estimates for A and alpha, I would need the historical data to find out the average number of calls for dinner I get on each day over the past few years. I cannot estimate the probability now..zzz.. I seriously wonder if this is what researchers do for fun?

have to cancel one and prepare to have dinner twice.