[Maths] Exponential Distribution

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I am confused by this. Mainly because our tutor has told us the function in the book is incorrect:

f(x) = λe^-λt

Where, λ = rate of occurance and t = time.

Our tutor says that it should actually be:

f(x) = e^-λt



I don't really understand the difference between them!! Can someone explain?

[sunburnt]

The PDF of an exponential distribution is λe^-λx or 1/βe^-x/β where λ=1/β. I'm not sure what your tutor is trying to get at...

[Andrew G]

Wikipedia Seems the book was right

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We have a list of questions to go through and I am still unclear as to which function to use. It appears there is a cumulative distribution function (1 − e ^{− λx}) and a probability distribution function (λe ^{− λx}). What is the difference and what are there applications?

I will post one of the questions later.

[sunburnt]

It's been a while since I did statistics, but if I recall correctly, this is the relation:
PDF: Probability Density Function. f(x)
CDF: Cumulative Distribution Function F(x)

X: a random number (in your case, from an exponential distribution)
x: the argument to the cdf or pdf function.

The PDF is a function, that when graphed, has area under the curve == 1. (in other words, the integral of f(x) of X from -inf to +inf is 1.)

The PDF f(x) represents the probability density -- the likelihood of a specific outcome to occur. This is not the probability that that specific outcome occurs!
Given a continuous distribution, the probability that our random number is exactly x is always 0.

The CDF F(x) of X == P(X <= x) ; ie that your random number X is at most x.

The exact relationship is that F(x) == integral from 0 to x of the pdf.

So suppose we have a random number X that represents the time until our product fails.

f(x) represents the likelihood that our product will fail at time x. (again, not the probability!)

F(b) represents the probability that our product will fail before or at time b.
1 - F(b) represents the probability that our product will not fail until after time b.

The integral from a to b of the pdf f(x) represents the probability that our product will fail between time a and time b. This is the same as F(b) - F(a)


Hope this is understandable. It's kind of late

Comprehension quiz:
can you see, looking at the statement: "The integral from a to b of the pdf f(x) represents the probability that our product will fail between time a and time b. " why I said earlier "the probability that our random number is exactly some z is always 0?"

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I think its because the scale is continuous i.e: two points in time and a measurement of time can only ever be between two points.

I will have a look at these quesitons later and let you know how I got on. I kind of understand your explanation. I just need to put the method into action

[rory]

ask your tutor where that will ever apply in the real world ..

[Valleysboy1978]

Hehe

The book has gone through multiple edits, and editors and proof-reading. It will be right.
As for your lecturer he's probably too stubborn to admit he's wrong....academics!

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Hehe

The book has gone through multiple edits, and editors and proof-reading. It will be right.
As for your lecturer he's probably too stubborn to admit he's wrong....academics!

The book was produced by our university. It has many errors, including spelling errors . I don't trust anything written in it

[MartinLiss]

Moved. Please don't post technical questions in the General Discussion / Chit Chat forum.

[sunburnt]

I think its because the scale is continuous i.e: two points in time and a measurement of time can only ever be between two points.

Bingo. To prove it, consider that the integral of the pdf from a to b is the probability that X falls between a and b. what is the integral of any function at a single point?

integral from a to a of f'(x) = f(x) - f(x) = 0.