Integral of exponential distribution from zero to infinity

  • Thread starter cooper607
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  • #1
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Homework Statement



here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...........(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a.........2)


Homework Equations


now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1........plz tell me if my value of A is ok or not........
and for the second problem how can i integrate those three components all together?
what is the formula, plz notify here......
thanks in advance



The Attempt at a Solution


A to be (-1/a*e^(x/a))
 

Answers and Replies

  • #2
tiny-tim
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hi cooper607! :smile:

you mean [itex][Ae^{-x/a}]_0^{infty}\ =\ 1[/itex]
… to solve the first one i found out A to be (-1/a*e^(x/a))

A is supposed to be a constant, how can it be a function of x ? :redface:
 
  • #3
371
0

Homework Statement



here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...........(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a.........2)


Homework Equations


now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1........plz tell me if my value of A is ok or not........
and for the second problem how can i integrate those three components all together?
what is the formula, plz notify here......
thanks in advance



The Attempt at a Solution


A to be (-1/a*e^(x/a))

No, its not ok. How is it even a value in the first place?
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
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Homework Statement



here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...........(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a.........2)


Homework Equations


now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1........plz tell me if my value of A is ok or not........
and for the second problem how can i integrate those three components all together?
what is the formula, plz notify here......
thanks in advance



The Attempt at a Solution


A to be (-1/a*e^(x/a))

Are A and a supposed to be constants? If so, then why would you equate A to (-1/a*e^(x/a))?

Let me ask a more fundamental question: have you studied integration? Both of the questions you ask are simple integration problems from introductory calculus. However, if you have not yet had that material, it would be understandable that you are having problems.

RGV
 
  • #5
HallsofIvy
Science Advisor
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The title of this thread says that the integral is from 0 to infinity. Did you not evaluate the anti-derivative at those values?
 

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