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

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

advice would be appreciated.

Reply 1

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)

Reply 2

Damien_Dalgaard

Original post by ludmila

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.

Reply 3

ludmila

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.

Reply 4

Damien_Dalgaard

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.

Thank you for your reply.

Reply 5

ludmila

Original post by Damien_Dalgaard

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).

Reply 6

Damien_Dalgaard

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!

Reply 7

ludmila

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 :wink:

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)

Reply 8

Damien_Dalgaard

Original post by ludmila

That's all right :wink:

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) = 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 :smile:

Reply 9

ludmila

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 :smile:

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) :smile:

Reply 10

Damien_Dalgaard

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) :smile: