Math Is Fun Forum

tyybo

Member

Registered: 2006-02-07

Posts: 6

Improper Integration is so fun..

Hey all. Im hoping i can find someone who really loves their calculus because i definetly have some. Any way this is the problem

Ok so im working with some probability type issues. and the first problem looks like this

Suppose that X is a continuous random variable over the interval 0,infinity with associated density fu8nction f(x)=0.03e^kx, k is just some constant.
  Calculate the Probability that X will be greater then 100. Result involves the constant K

So after some gritting i figured this part out. I know the entire probablility has to equal 1 for 100 percent. and being that you cant really figure out infinity i decided to do the integral of 0-100 of the density function. and i got that whole mess to be

   1 times .03e^k*100    minus       1 times .03e^k*0
   K                                               k       

Now i need to find k which is really messing with me.
I got a hit from my teacher to use an improper integral(not erally sure on what this is)

any way this is how he has me set up and this is where im stuck

the integral of 0 to "b" of the density function=       .03    e^k*x evaluated from 0-b
                                                                          k
and then he has written what happens as b approaches infinity.  So now, im pretty lost, so any one who relaly wants to take the time to read this, id really appretiate it. thanks all!

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Improper Integration is so fun..

Are you asking what is the probability f(x) is over 100 or just x?  Because if it just x, then the function doesn't matter, you said it was a random continuous variable, so 1/2 of the time x is > 100 and 1/2 of the time x < 100 since x can go from negative infinity to postive infinity.

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