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# S2 Binomial Distribution (easy question) watch

1. Can someone tell me why for question d) you do the sum p(x<_7)-p(x<_1) as opposed to using p(x<2) thankyou
2. (Original post by Abby5001)
Can someone tell me why for question d) you do the sum p(x<_7)-p(x<_1) as opposed to using p(x<2) thankyou
P(x <=1) = P(x<2) since the binomial is a discrete distribution; x can only be an integer so saying x is less than 2 means x must be 1 or 0.
3. (Original post by 16Characters....)
P(x <=1) = P(x<2) since the binomial is a discrete distribution; x can only be an integer so saying x is less than 2 means x must be 1 or 0.
I understand what you are saying but x is not less than 2 according to the signs surely? It's less than or equal to?
4. (Original post by Abby5001)
I understand what you are saying but x is not less than 2 according to the signs surely? It's less than or equal to?
I apologise, my response was clumsily worded.

You are finding P(2 <= x <= 7) so you are finding the probability that x = 2, 3, 4, 5, 6, or 7. P(x <=7) finds the probability that x = 0, 1, 2, 3,..., 7 which is including the values of x less than 2, which you did not want. So you subtract P(x < 2). Which is equivalent to P(x <= 1).
5. (Original post by 16Characters....)
I apologise, my response was clumsily worded.

You are finding P(2 <= x <= 7) so you are finding the probability that x = 2, 3, 4, 5, 6, or 7. P(x <=7) finds the probability that x = 0, 1, 2, 3,..., 7 which is including the values of x less than 2, which you did not want. So you subtract P(x < 2). Which is equivalent to P(x <= 1).
Right thankyou that was very helpful but what is the reason why x<_1 is used rather than x<2?
6. (Original post by Abby5001)
Right thankyou that was very helpful but what is the reason why x<_1 is used rather than x<2?
Well you could have used either, they are as I said equivalent probabilities. I suspect P(x <=1) is used as it is clearer what you are actually doing, especially if you are using the cumulative probability tables.
7. (Original post by 16Characters....)
Well you could have used either, they are as I said equivalent probabilities. I suspect P(x <=1) is used as it is clearer what you are actually doing, especially if you are using the cumulative probability tables.
great I see, thanks again

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