Mathematical expectation question

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Following are the results obtained for two independent random variable x and y. $E(x)=4,E(y)=6,v(x)=5$ and $V(y)=4$, so find the value of



$1) $ $E(2x-y)^2$



$2) $ $E(7-2x-5y)$



That's the way I am trying :



$$V(x)=E(x^2)-E(x)^2 $$



$$5=E(x^2)-16$$
$$E(x^2)=21$$
In the same way
$$E(y^2)=40$$
$$E(xy)=6times 4=24$$



beginalignE(2x-y)^2 &=4E(x^2)-4E(xy)+E(y^2) \
&=4(21)-4(24)+40\
&=84-96+40\
&=28
endalign
But actual answer is $60$ which doesn't match.







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  • As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
    – Siong Thye Goh
    Aug 27 at 15:43















up vote
0
down vote

favorite












Following are the results obtained for two independent random variable x and y. $E(x)=4,E(y)=6,v(x)=5$ and $V(y)=4$, so find the value of



$1) $ $E(2x-y)^2$



$2) $ $E(7-2x-5y)$



That's the way I am trying :



$$V(x)=E(x^2)-E(x)^2 $$



$$5=E(x^2)-16$$
$$E(x^2)=21$$
In the same way
$$E(y^2)=40$$
$$E(xy)=6times 4=24$$



beginalignE(2x-y)^2 &=4E(x^2)-4E(xy)+E(y^2) \
&=4(21)-4(24)+40\
&=84-96+40\
&=28
endalign
But actual answer is $60$ which doesn't match.







share|cite|improve this question






















  • As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
    – Siong Thye Goh
    Aug 27 at 15:43













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Following are the results obtained for two independent random variable x and y. $E(x)=4,E(y)=6,v(x)=5$ and $V(y)=4$, so find the value of



$1) $ $E(2x-y)^2$



$2) $ $E(7-2x-5y)$



That's the way I am trying :



$$V(x)=E(x^2)-E(x)^2 $$



$$5=E(x^2)-16$$
$$E(x^2)=21$$
In the same way
$$E(y^2)=40$$
$$E(xy)=6times 4=24$$



beginalignE(2x-y)^2 &=4E(x^2)-4E(xy)+E(y^2) \
&=4(21)-4(24)+40\
&=84-96+40\
&=28
endalign
But actual answer is $60$ which doesn't match.







share|cite|improve this question














Following are the results obtained for two independent random variable x and y. $E(x)=4,E(y)=6,v(x)=5$ and $V(y)=4$, so find the value of



$1) $ $E(2x-y)^2$



$2) $ $E(7-2x-5y)$



That's the way I am trying :



$$V(x)=E(x^2)-E(x)^2 $$



$$5=E(x^2)-16$$
$$E(x^2)=21$$
In the same way
$$E(y^2)=40$$
$$E(xy)=6times 4=24$$



beginalignE(2x-y)^2 &=4E(x^2)-4E(xy)+E(y^2) \
&=4(21)-4(24)+40\
&=84-96+40\
&=28
endalign
But actual answer is $60$ which doesn't match.









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 27 at 16:35









Siong Thye Goh

81k1453102




81k1453102










asked Aug 27 at 15:06









Aayush Mukharji

214




214











  • As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
    – Siong Thye Goh
    Aug 27 at 15:43

















  • As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
    – Siong Thye Goh
    Aug 27 at 15:43
















As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
– Siong Thye Goh
Aug 27 at 15:43





As you may have noticed, most of your posts was closed down. Do not just paste the question statement as shown in a typical homework format on the site. Include your thoughts and attempts. It is good to include your working in the original post as compared to telling us what you have found without showing us the working. Take it as an exercise to edit the post to include the working so that one of us can tell where you make the mistake if there is any. Also, textbooks do make mistakes.
– Siong Thye Goh
Aug 27 at 15:43











2 Answers
2






active

oldest

votes

















up vote
0
down vote



accepted










For the first part,beginalign
E[(2X-Y)^2] &= Var((2X-Y)) + [E(2X-Y)]^2 \
&= 4Var(X)+Var(Y)+(2E(X)-E(Y))^2
endalign






share|cite|improve this answer




















  • I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
    – Aayush Mukharji
    Aug 27 at 16:28










  • your answer is correct.
    – Siong Thye Goh
    Aug 27 at 16:32










  • Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
    – Aayush Mukharji
    Aug 27 at 16:34










  • what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
    – Siong Thye Goh
    Aug 27 at 16:38











  • Thanks you very much you are really kind and helpful.
    – Aayush Mukharji
    Aug 27 at 16:40

















up vote
0
down vote













Hint: For independent random variables, $E[XY]=E[X]cdot E[Y]$.






share|cite|improve this answer




















  • I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
    – Aayush Mukharji
    Aug 27 at 15:16










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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote



accepted










For the first part,beginalign
E[(2X-Y)^2] &= Var((2X-Y)) + [E(2X-Y)]^2 \
&= 4Var(X)+Var(Y)+(2E(X)-E(Y))^2
endalign






share|cite|improve this answer




















  • I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
    – Aayush Mukharji
    Aug 27 at 16:28










  • your answer is correct.
    – Siong Thye Goh
    Aug 27 at 16:32










  • Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
    – Aayush Mukharji
    Aug 27 at 16:34










  • what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
    – Siong Thye Goh
    Aug 27 at 16:38











  • Thanks you very much you are really kind and helpful.
    – Aayush Mukharji
    Aug 27 at 16:40














up vote
0
down vote



accepted










For the first part,beginalign
E[(2X-Y)^2] &= Var((2X-Y)) + [E(2X-Y)]^2 \
&= 4Var(X)+Var(Y)+(2E(X)-E(Y))^2
endalign






share|cite|improve this answer




















  • I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
    – Aayush Mukharji
    Aug 27 at 16:28










  • your answer is correct.
    – Siong Thye Goh
    Aug 27 at 16:32










  • Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
    – Aayush Mukharji
    Aug 27 at 16:34










  • what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
    – Siong Thye Goh
    Aug 27 at 16:38











  • Thanks you very much you are really kind and helpful.
    – Aayush Mukharji
    Aug 27 at 16:40












up vote
0
down vote



accepted







up vote
0
down vote



accepted






For the first part,beginalign
E[(2X-Y)^2] &= Var((2X-Y)) + [E(2X-Y)]^2 \
&= 4Var(X)+Var(Y)+(2E(X)-E(Y))^2
endalign






share|cite|improve this answer












For the first part,beginalign
E[(2X-Y)^2] &= Var((2X-Y)) + [E(2X-Y)]^2 \
&= 4Var(X)+Var(Y)+(2E(X)-E(Y))^2
endalign







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 27 at 15:40









Siong Thye Goh

81k1453102




81k1453102











  • I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
    – Aayush Mukharji
    Aug 27 at 16:28










  • your answer is correct.
    – Siong Thye Goh
    Aug 27 at 16:32










  • Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
    – Aayush Mukharji
    Aug 27 at 16:34










  • what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
    – Siong Thye Goh
    Aug 27 at 16:38











  • Thanks you very much you are really kind and helpful.
    – Aayush Mukharji
    Aug 27 at 16:40
















  • I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
    – Aayush Mukharji
    Aug 27 at 16:28










  • your answer is correct.
    – Siong Thye Goh
    Aug 27 at 16:32










  • Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
    – Aayush Mukharji
    Aug 27 at 16:34










  • what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
    – Siong Thye Goh
    Aug 27 at 16:38











  • Thanks you very much you are really kind and helpful.
    – Aayush Mukharji
    Aug 27 at 16:40















I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
– Aayush Mukharji
Aug 27 at 16:28




I did this way answer comes 28. Is it correct or not please tell me.Because my answer is not matching to the book answer .
– Aayush Mukharji
Aug 27 at 16:28












your answer is correct.
– Siong Thye Goh
Aug 27 at 16:32




your answer is correct.
– Siong Thye Goh
Aug 27 at 16:32












Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
– Aayush Mukharji
Aug 27 at 16:34




Thanks. But lot of people writing in comments that my questions are not asked in prescribed format and I am not showing my workings. Actually I am new to this site. Can you guide me about asking questions.
– Aayush Mukharji
Aug 27 at 16:34












what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
– Siong Thye Goh
Aug 27 at 16:38





what most people are looking for is what you have attempted so far. Here is a link on how to ask a question on the site. Most of the time just try your best to include your working in mathjax. It is alright if your attempt is wrong. Welcome to MSE.
– Siong Thye Goh
Aug 27 at 16:38













Thanks you very much you are really kind and helpful.
– Aayush Mukharji
Aug 27 at 16:40




Thanks you very much you are really kind and helpful.
– Aayush Mukharji
Aug 27 at 16:40










up vote
0
down vote













Hint: For independent random variables, $E[XY]=E[X]cdot E[Y]$.






share|cite|improve this answer




















  • I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
    – Aayush Mukharji
    Aug 27 at 15:16














up vote
0
down vote













Hint: For independent random variables, $E[XY]=E[X]cdot E[Y]$.






share|cite|improve this answer




















  • I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
    – Aayush Mukharji
    Aug 27 at 15:16












up vote
0
down vote










up vote
0
down vote









Hint: For independent random variables, $E[XY]=E[X]cdot E[Y]$.






share|cite|improve this answer












Hint: For independent random variables, $E[XY]=E[X]cdot E[Y]$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 27 at 15:11









paw88789

28.3k12248




28.3k12248











  • I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
    – Aayush Mukharji
    Aug 27 at 15:16
















  • I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
    – Aayush Mukharji
    Aug 27 at 15:16















I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
– Aayush Mukharji
Aug 27 at 15:16




I tried this but my answer comes 28 which doesn't match the actual answer is it me wrong or actual answer?
– Aayush Mukharji
Aug 27 at 15:16

















 

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