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Ok... Lets do it this way:
And if I collapse rows with same number of people as a union of the two probabilities I receive:
Still no 1.0 in the total. What is wrong now?
Try using the exact values. And, also, it should be a 2 there, not a 5.
I am not sure I understand. If we say that for the "exactly one group is late" we need to calculate: intersection of "one group is late" and "four groups are not late", and any of the five groups can be late. So the formula for the one group become:
But once I recalculate whole table like this - the sum become 1.98.
Those probabilities are not correct. The problem is that if you want exactly one person to be late, you only get the probability that one of the two is late, but not that everybody else isn't.
I am reading and rereading the textbook and I still do not understand what exactly is the pmf and cdf?
Since there are two possible combinations for 2, 4, and 6 people, we need to take a union of probabilities for these combinations and final P(X) become this:
And from here I need to find pmf
All examples in the textbook are just doing direct substitution p(x)=P(X=x) but if I summarize my P(X) I receive 1.4575616. And sum of p(x) for all x is supposed to be equal 1.0...
So, did I make a mistake somewhere or what am I missing?