Finding Variance of joint probability function

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I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$frac125x^218,; 0le xle 0.6,;frac910x^2,; (0.6le xle 0.9), text and 0 text elsewhere.$$ I know how to find the variance for a single probability function, however not when they consist of two functions.



Help will be appreciated. Thanks.




variance




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  • Use $Var[X] = E[X^2] - (E[X])^2$
    – the man
    Aug 29 at 11:06










  • That is not a joint probability function. It is a piecewise function.
    – Graham Kemp
    Aug 29 at 11:34














up vote
0
down vote

favorite












I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$frac125x^218,; 0le xle 0.6,;frac910x^2,; (0.6le xle 0.9), text and 0 text elsewhere.$$ I know how to find the variance for a single probability function, however not when they consist of two functions.



Help will be appreciated. Thanks.




variance




share|cite|improve this question






















  • Use $Var[X] = E[X^2] - (E[X])^2$
    – the man
    Aug 29 at 11:06










  • That is not a joint probability function. It is a piecewise function.
    – Graham Kemp
    Aug 29 at 11:34












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$frac125x^218,; 0le xle 0.6,;frac910x^2,; (0.6le xle 0.9), text and 0 text elsewhere.$$ I know how to find the variance for a single probability function, however not when they consist of two functions.



Help will be appreciated. Thanks.




variance




share|cite|improve this question














I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$frac125x^218,; 0le xle 0.6,;frac910x^2,; (0.6le xle 0.9), text and 0 text elsewhere.$$ I know how to find the variance for a single probability function, however not when they consist of two functions.



Help will be appreciated. Thanks.





variance





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share|cite|improve this question








edited Aug 29 at 11:23









amWhy

190k26221433




190k26221433










asked Aug 29 at 10:45









Deep Patel

63




63











  • Use $Var[X] = E[X^2] - (E[X])^2$
    – the man
    Aug 29 at 11:06










  • That is not a joint probability function. It is a piecewise function.
    – Graham Kemp
    Aug 29 at 11:34
















  • Use $Var[X] = E[X^2] - (E[X])^2$
    – the man
    Aug 29 at 11:06










  • That is not a joint probability function. It is a piecewise function.
    – Graham Kemp
    Aug 29 at 11:34















Use $Var[X] = E[X^2] - (E[X])^2$
– the man
Aug 29 at 11:06




Use $Var[X] = E[X^2] - (E[X])^2$
– the man
Aug 29 at 11:06












That is not a joint probability function. It is a piecewise function.
– Graham Kemp
Aug 29 at 11:34




That is not a joint probability function. It is a piecewise function.
– Graham Kemp
Aug 29 at 11:34










1 Answer
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You are given a piecewise probability density function: $$f_X(x)=begincases 125 x^2/18 &:& ~~~0leq xlt 0.6\ 9/(10x^2)&:& 0.6leq xleq 0.9\0&:&textrmelsewhereendcases$$



To find an expected value, you simply integrate over the partitions using the relevant function and add: $$mathsf E(g(X)) = int_0^0.6 125x^2~g(x)/18~mathsf dx + int_0.6^0.9 9~g(x)/(10x^2)~mathsf d x$$



Now evaluate: $mathsfVar(X)=mathsf E(X^2)-mathsf E(X)^2$






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  • what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
    – Deep Patel
    Aug 29 at 12:24










  • @DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
    – Graham Kemp
    Aug 29 at 21:01










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1 Answer
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1 Answer
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active

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active

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up vote
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You are given a piecewise probability density function: $$f_X(x)=begincases 125 x^2/18 &:& ~~~0leq xlt 0.6\ 9/(10x^2)&:& 0.6leq xleq 0.9\0&:&textrmelsewhereendcases$$



To find an expected value, you simply integrate over the partitions using the relevant function and add: $$mathsf E(g(X)) = int_0^0.6 125x^2~g(x)/18~mathsf dx + int_0.6^0.9 9~g(x)/(10x^2)~mathsf d x$$



Now evaluate: $mathsfVar(X)=mathsf E(X^2)-mathsf E(X)^2$






share|cite|improve this answer




















  • what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
    – Deep Patel
    Aug 29 at 12:24










  • @DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
    – Graham Kemp
    Aug 29 at 21:01














up vote
2
down vote













You are given a piecewise probability density function: $$f_X(x)=begincases 125 x^2/18 &:& ~~~0leq xlt 0.6\ 9/(10x^2)&:& 0.6leq xleq 0.9\0&:&textrmelsewhereendcases$$



To find an expected value, you simply integrate over the partitions using the relevant function and add: $$mathsf E(g(X)) = int_0^0.6 125x^2~g(x)/18~mathsf dx + int_0.6^0.9 9~g(x)/(10x^2)~mathsf d x$$



Now evaluate: $mathsfVar(X)=mathsf E(X^2)-mathsf E(X)^2$






share|cite|improve this answer




















  • what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
    – Deep Patel
    Aug 29 at 12:24










  • @DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
    – Graham Kemp
    Aug 29 at 21:01












up vote
2
down vote










up vote
2
down vote









You are given a piecewise probability density function: $$f_X(x)=begincases 125 x^2/18 &:& ~~~0leq xlt 0.6\ 9/(10x^2)&:& 0.6leq xleq 0.9\0&:&textrmelsewhereendcases$$



To find an expected value, you simply integrate over the partitions using the relevant function and add: $$mathsf E(g(X)) = int_0^0.6 125x^2~g(x)/18~mathsf dx + int_0.6^0.9 9~g(x)/(10x^2)~mathsf d x$$



Now evaluate: $mathsfVar(X)=mathsf E(X^2)-mathsf E(X)^2$






share|cite|improve this answer












You are given a piecewise probability density function: $$f_X(x)=begincases 125 x^2/18 &:& ~~~0leq xlt 0.6\ 9/(10x^2)&:& 0.6leq xleq 0.9\0&:&textrmelsewhereendcases$$



To find an expected value, you simply integrate over the partitions using the relevant function and add: $$mathsf E(g(X)) = int_0^0.6 125x^2~g(x)/18~mathsf dx + int_0.6^0.9 9~g(x)/(10x^2)~mathsf d x$$



Now evaluate: $mathsfVar(X)=mathsf E(X^2)-mathsf E(X)^2$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 29 at 11:46









Graham Kemp

81.1k43275




81.1k43275











  • what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
    – Deep Patel
    Aug 29 at 12:24










  • @DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
    – Graham Kemp
    Aug 29 at 21:01
















  • what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
    – Deep Patel
    Aug 29 at 12:24










  • @DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
    – Graham Kemp
    Aug 29 at 21:01















what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
– Deep Patel
Aug 29 at 12:24




what is the g(x) in the E(X) for. What does it represent, i have never come across this before. Also, i have never come across the equation Var(X) = E(X^2) - E(X)^2
– Deep Patel
Aug 29 at 12:24












@DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
– Graham Kemp
Aug 29 at 21:01




@DeepPatel $g(X)$ is a function of the random variable: substitute the function you require. $mathsf Var(X)=mathsf E(X)-mathsf E(X)^2$ is the second equation for variance which you should memorise. Perhaps the first, depending on your teacher. The other is $mathsf Var(X)=mathsf E((X-mathsf E(X))^2)$
– Graham Kemp
Aug 29 at 21:01

















 

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