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# S2 - can you explain something to me... watch

1. P(X≥4)=1-P(X≤3)
i cant understand this,
P(X≥4)=1-P(X≤4) makes more sense to me
cos if we draw the graph, where area under the graph = probability=1, and mark the region X≥4, i dont see how its possible to get X≥4 by 1-(X≤3)
2. Basically its cos binomial distribution is discrete not continuous so you have to use consecutive integers.....i think

can anyone else confirm?
3. P(X≥3) = P(X=3) + P(X=4) + P(X=5) etc

P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

They would both include X=3, so it's P(X≤2).

Although I find it easier to look at as P(X≥3) = 1 - P(X<3)

and P(X<3) = P(X≤2) for discrete distributions.

Dunno why and maybe it's just me prefers to think of it like that
4. (Original post by Adil Bhai)
Basically its cos binomial distribution is discrete not continuous so you have to use consecutive integers.....i think

can anyone else confirm?
Yes thats true. If you're using integers then what you say is true; whereas with continuous data the 2nd equation is correct.
5. P(X >= 4) = 1 - P(X < 4) is always true, because exactly one of the events {X >= 4} and {X < 4} must occur.

If X is integer-valued then P(X < 4) = P(X <=3) so P(X >= 4) = 1 - P(X <= 3).
6. (Original post by RussianDude)
P(X≥4)=1-P(X≤3)
i cant understand this,
P(X≥4)=1-P(X≤4) makes more sense to me
cos if we draw the graph, where area under the graph = probability=1, and mark the region X≥4, i dont see how its possible to get X≥4 by 1-(X≤3)
The distribution is discrete, not continuous.
Ok, think about it this way. below there are 10 dots, labelled 1 to 10, they represent a probability distribution, so their sum is 1.

1 2 3 4 5 6 7 8 9 10
o o o o o o o o o o

P(X≥5) are the numbers 5 to 10, right? This is also the same as 1 (i.e. everything) - P(X≤4)

So, in essence P(X≥x) = 1 - P(X≤x-1)
7. thanks guys, now i get it

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