find the expected value of g(x)  TOPIC_SOLVED

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find the expected value of g(x)

Postby zorro on Sat Jun 26, 2010 6:21 am

Problem : If the probability of X is given by


find the expected value of

Solution :



is this process which i am following is it correct or no?
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Re: find the expected value of g(x)

Postby jk22 on Sat Jun 26, 2010 1:43 pm

Hallo, nice to meet you. >I'm new on this forum.

For me this process of calculation is correct, even if there is a way to see the things that I'm not sure about :

We need <g(X)=Y>=<Y>, and then we need the probability density of Y. I don't know if this gives the same result. (We know that Y runs over [-13/4;3] if x runs over [0;3]).

From this we see there could appear a problem if g were not bijective.

See you soon, with friendly greetings.
Last edited by jk22 on Sat Jun 26, 2010 1:55 pm, edited 1 time in total.
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Re: find the expected value of g(x)

Postby maggiemagnet on Sat Jun 26, 2010 1:47 pm

According to this Wikipedia article, yes, it looks like you have set this up correctly. Do you need any help with the integrations?
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Re: find the expected value of g(x)  TOPIC_SOLVED

Postby jk22 on Sat Jun 26, 2010 2:47 pm

Hallo, nice to meet you too.

Thanks for the reference. Me I lost myself in : should I calculate like this :

y=g(x), then :



and hence we find the distribution of Y : f_y(g(x))g'(x)=f(x), or f_y(y)=f(g^-1(y))/g'(g^-1(y)), to get the same as above.
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Re: find the expected value of g(x)

Postby zorro on Sun Jun 27, 2010 7:23 am

THANKS GUYS FOR ALL UR POST ......I JUST NEEDED TO CHECK IF I WAS DOING IT CORRECTLY OR NO ...... :clap:
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