Thread: Basic algebra but dont know what a euler number is?

Assume P(C2) = eP(C1) (where e is the Euler number ln(e) = 1)

And i know P(C2) + P(C1) = 1

find P(C2) and P(C1)

Thanks.

Originally Posted by adam_leeds

Assume P(C2) = eP(C1) (where e is the Euler number ln(e) = 1)

And i know P(C2) + P(C1) = 1

find P(C2) and P(C1)

Thanks.

Well there are Euler numbers and then there's Euler's number. Here you are asked about Euler's number which is just a constant (a real number with interesting properties). What are P(Ci) supposed to represent? I don't see why it's not just a system of equations.

a = eb
a + b = 1

Find a and b.

Originally Posted by adam_leeds

Assume P(C2) = eP(C1) (where e is the Euler number ln(e) = 1)

And i know P(C2) + P(C1) = 1

find P(C2) and P(C1)

Thanks.

The question tells you what e is (in this case the base for the natural logarithm)

CB

Is it lnP(C2) = P(C1)

lnP(C2) + P(C2) = 1

P(C2) = 1 and P(C1) = 0?

Originally Posted by adam_leeds

Is it lnP(C2) = P(C1)

lnP(C2) + P(C2) = 1

P(C2) = 1 and P(C1) = 0?

There is a mistake with your first step, would be lnP(C2) = 1 + P(C1).

But easiest way in my opinion to start is substitution to get eP(C1) + P(C1) = 1.

I don't understand

Whats P(C1) and P(C2) Can someone do it step by step for me please, thanks.

Originally Posted by adam_leeds

I don't understand

Whats P(C1) and P(C2) Can someone do it step by step for me please, thanks.

I asked in my first post what P(Ci) represent and you didn't respond to that, but assuming they're just real numbers,

P(C2) = eP(C1)
P(C2) + P(C1) = 1

substitute

eP(C1) + P(C1) = 1

P(C1)(e + 1) = 1

P(C1) = 1/(e+1)

then

P(C2) = eP(C1) = e/(e+1)

Whats the point in telling us ln(e) = 1 , if you haven't used it?

Originally Posted by adam_leeds

Whats the point in telling us ln(e) = 1 , if you haven't used it?

There's no real point if P(Ci) are just real numbers but if they represent something else or if you gave us more context then maybe it would matter.

Originally Posted by undefined

There's no real point if P(Ci) are just real numbers but if they represent something else or if you gave us more context then maybe it would matter.

Ok thanks, the whole question

Consider a 2-class problem with two-dimensional features (x1,x2)transposed . The class conditional distributions P(x|Ci) are modelled by gaussian densities means = (-1,1) transposed and (1,1) transposed respectively with identical covariance matrices.

Assume P(C2) = eP(C1) (where e is the Euler number ln(e) = 1) and use the logistic discriminant fuction to derive the explicit expression of P(C1|x)

Originally Posted by adam_leeds

Ok thanks, the whole question

Consider a 2-class problem with two-dimensional features (x1,x2)transposed . The class conditional distributions P(x|Ci) are modelled by gaussian densities means = (-1,1) transposed and (1,1) transposed respectively with identical covariance matrices.

Assume P(C2) = eP(C1) (where e is the Euler number ln(e) = 1) and use the logistic discriminant fuction to derive the explicit expression of P(C1|x)

That changes things significantly.

I'm going to have to pass on this one, not too familiar with the territory.