Random Variables (expectation value, var(x) and standard deviation
Consider the random variables X
x 1 | 2 | 3
P(x) 0.3 |0.5 |0.2
Find the distribution, mean
µY , variance and standard deviation σY of the random variable Y = Φ(X) where
(a) Φ(x) = x^3 (b) Φ(x) = 2^x.
My question is. When i will calculate the expectation value..will i have to do it based on the table above which is the distribution of x, or i have to calculate it based on the table of x^3?
random-variables
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
add a comment |
Consider the random variables X
x 1 | 2 | 3
P(x) 0.3 |0.5 |0.2
Find the distribution, mean
µY , variance and standard deviation σY of the random variable Y = Φ(X) where
(a) Φ(x) = x^3 (b) Φ(x) = 2^x.
My question is. When i will calculate the expectation value..will i have to do it based on the table above which is the distribution of x, or i have to calculate it based on the table of x^3?
random-variables
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07
add a comment |
Consider the random variables X
x 1 | 2 | 3
P(x) 0.3 |0.5 |0.2
Find the distribution, mean
µY , variance and standard deviation σY of the random variable Y = Φ(X) where
(a) Φ(x) = x^3 (b) Φ(x) = 2^x.
My question is. When i will calculate the expectation value..will i have to do it based on the table above which is the distribution of x, or i have to calculate it based on the table of x^3?
random-variables
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
Consider the random variables X
x 1 | 2 | 3
P(x) 0.3 |0.5 |0.2
Find the distribution, mean
µY , variance and standard deviation σY of the random variable Y = Φ(X) where
(a) Φ(x) = x^3 (b) Φ(x) = 2^x.
My question is. When i will calculate the expectation value..will i have to do it based on the table above which is the distribution of x, or i have to calculate it based on the table of x^3?
random-variables
random-variables
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
edited Dec 28 '18 at 14:11
Anastasia Kyriakou
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
asked Dec 28 '18 at 14:02
Anastasia KyriakouAnastasia Kyriakou
12
12
What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07
add a comment |
What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07
What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07
add a comment |
1 Answer
1
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votes
Guide:
Apply: $$mathbb Ef(X)=sum_x f(x)P(X=x)$$
In your case just a sum of $3$ terms, so calculators are not needed.
This in order to find $mathbb EPhi(X)$ and $mathbb EPhi(X)^2$.
Then you can also find variance and standard deviation.
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
|
show 7 more comments
Your Answer
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1 Answer
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1 Answer
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active
oldest
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active
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active
oldest
votes
Guide:
Apply: $$mathbb Ef(X)=sum_x f(x)P(X=x)$$
In your case just a sum of $3$ terms, so calculators are not needed.
This in order to find $mathbb EPhi(X)$ and $mathbb EPhi(X)^2$.
Then you can also find variance and standard deviation.
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
|
show 7 more comments
Guide:
Apply: $$mathbb Ef(X)=sum_x f(x)P(X=x)$$
In your case just a sum of $3$ terms, so calculators are not needed.
This in order to find $mathbb EPhi(X)$ and $mathbb EPhi(X)^2$.
Then you can also find variance and standard deviation.
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
|
show 7 more comments
Guide:
Apply: $$mathbb Ef(X)=sum_x f(x)P(X=x)$$
In your case just a sum of $3$ terms, so calculators are not needed.
This in order to find $mathbb EPhi(X)$ and $mathbb EPhi(X)^2$.
Then you can also find variance and standard deviation.
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
Guide:
Apply: $$mathbb Ef(X)=sum_x f(x)P(X=x)$$
In your case just a sum of $3$ terms, so calculators are not needed.
This in order to find $mathbb EPhi(X)$ and $mathbb EPhi(X)^2$.
Then you can also find variance and standard deviation.
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
answered Dec 28 '18 at 14:08
drhabdrhab
98.4k544129
98.4k544129
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
|
show 7 more comments
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
Yes but when i will calculate the expectation value, will i do : 1*0.3+2*0.5+3*0.2 or i will do 1*0.3+4*0.5+9*0.2 because it says Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:14
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
The first calculation in your comment is a calculation of $mathbb EX=sum_xxP(X=x)$ and the second is a calculation of $mathbb EX^2=sum_xx^2P(X=x)$. Since $Phi(x)=x^3$ you should go for $mathbb EPhi(X)=mathbb EX^3=sum_xx^3P(X=x)$.
– drhab
Dec 28 '18 at 14:17
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
Okay and if i use only the table of x and x^2 of course to find the variance, where will i use the Φ(x) = x^3 ?
– Anastasia Kyriakou
Dec 28 '18 at 14:19
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
$mathsf{Var}(Phi(X))=mathbb EPhi(X)^2-(mathbb EPhi(X))^2$. You already found $mathbb EPhi(X)$ so it remains to find $mathbb EPhi(X)^2=mathbb EX^6$.This with the same method.
– drhab
Dec 28 '18 at 14:21
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
yes i know how to calculate.but why the question says for Φ(x) = x^3? what does change?
– Anastasia Kyriakou
Dec 28 '18 at 14:24
|
show 7 more comments
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What is the distribution of $X$?
– Jonas
Dec 28 '18 at 14:03
i have added it
– Anastasia Kyriakou
Dec 28 '18 at 14:07