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# Statistics range values i.e. P(1 <= X <= 4) watch

1. So for the probability that 1 is less than and equal to X is less than equal to 4.

I get:

P(X<= 4) - P(X>=1)

= P(X<= 4) - ( 1 - P (X < 1)

But this is wrong and I don't know why.

Why is it P(X <= 0) ?

smh

2. P(1<=X<=4) is P(X=1 or X=2 or X=3 or X=4)

P(X<=4) is P(X=0 or X=1 or X=2 or X=3 or X=4)

So P(1<=X<=4) = P(X<=4) - P(X=0)

( probability P(X=0) is the same as probability P(X<=0) since X can't be negative)
3. (Original post by ludmila)
P(1<=X<=4) is P(X=1 or X=2 or X=3 or X=4)

P(X<=4) is P(X=0 or X=1 or X=2 or X=3 or X=4)

So P(1<=X<=4) = P(X<=4) - P(X=0)

( probability P(X=0) is the same as probability P(X<=0) since X can't be negative)
Thank you for your explanation. Since P(1 <= X) is the the same as the P ( X<1) = P(X=0).

Is this correct, I see what you mean, thanks.
4. (Original post by Damien_Dalgaard)
Thank you for your explanation. Since P(1 <= X) is the the same as the P ( X<1) = P(X=0).

Is this correct, I see what you mean, thanks.
P(1<=X) can't be the same as P(X<1).
Always think what values X can have.
P(1<=X) is the probability that X will be either 0 or 1.
P(1<X) is the probability that X will be 0 only.
5. (Original post by ludmila)
P(1<=X) can't be the same as P(X<1).
Always think what values X can have.
P(1<=X) is the probability that X will be either 0 or 1.
P(1<X) is the probability that X will be 0 only.
Sorry I meant to say P(1<=X) is the same as P(X>=1) which is the same as 1 - P(X <=1)

Is that right?

I am confused, if the probability of 1 is less than or equal to x, that must mean that x is greater than or equal to 1. Therefore the lowest value that will satisify that will be 1.

Is this for discrete values only as well.

6. (Original post by Damien_Dalgaard)
Sorry I meant to say P(1<=X) is the same as P(X>=1) which is the same as 1 - P(X <=1)

Is that right?

I am confused, if the probability of 1 is less than or equal to x, that must mean that x is greater than or equal to 1. Therefore the lowest value that will satisify that will be 1.

Is this for discrete values only as well.

OOOh, sorry, I didn't notice you used 1<=X (I always write is as X>=1 so didn't even think before I answered). Of course P(1<=X) is the same as P(X>=1) = 1 - P(X <1). But you can't say that P(1<=X<=4) = P(X<= 4) - P(X>=1).
7. (Original post by ludmila)
OOOh, sorry, I didn't notice you used 1<=X (I always write is as X>=1 so didn't even think before I answered). Of course P(1<=X) is the same as P(X>=1) = 1 - P(X <=1). But you can't say that P(1<=X<=4) = P(X<= 4) - P(X>=1).
Sorry is it that (the part in bold).

Right but from P(1<=X<=4) = P(X<= 4) - P(X>=1)

Is it P(X<= 4) - ( 1 - (P X <= 1)

So sorry to keep bothering you but this keeps frazzling me!
8. (Original post by Damien_Dalgaard)
Sorry is it that (the part in bold).

Right but from P(1<=X<=4) = P(X<= 4) - P(X>=1)

Is it P(X<= 4) - ( 1 - (P X <= 1)

So sorry to keep bothering you but this keeps frazzling me!
That's all right

a) P(X>=1) = 1 - P(X <1) (not
P(X>=1) = 1 - P(X <=1) because you want to calculate probability when X is 1, 2, 3, .... By writing 1 - P(X <=1) you are excluding the option X=1.

b) P(1<=X<=4) does NOT equal P(X<= 4) - P(X>=1).

P(1<=X<=4) = P(X<= 4) - P(X<1) = P(X<=4) - P(X=0)
9. (Original post by ludmila)
That's all right

a) P(X>=1) = 1 - P(X <1) (not P(X>=1) = 1 - P(X <=1) because you want to calculate probability when X is 1, 2, 3, .... By writing 1 - P(X <=1) you are excluding the option X=1.

b) [/FONT][/FONT]
P(1<=X<=4) = P(X<= 4) - P(X<1) = P(X<=4) - P(X=0)

omg of course, I see it now.

I've also done a number line and I can see it from there too.

Thank you so much.

Last last question this is for discrete probablities so applicable to binomial and poisson distribution, so we do not have to worry about the probability between 0 and 1 itself right.

Are you doing S2/S3
10. (Original post by Damien_Dalgaard)
omg of course, I see it now.

I've also done a number line and I can see it from there too.

Thank you so much.

Last last question this is for discrete probablities so applicable to binomial and poisson distribution, so we do not have to worry about the probability between 0 and 1 itself right.

Are you doing S2/S3
No, you don't need to worry about decimals when dealing with discrete probabilities.

I'm self-studying S1 and S2 (and the rest of the A level)
11. (Original post by ludmila)
No, you don't need to worry about decimals when dealing with discrete probabilities.

I'm self-studying S1 and S2 (and the rest of the A level)

Thought so thanks for the clarity, ah nice am self studying.

s2

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