Mixing
E[(X+Y)^3], where X follows exponential distribution with a, and Y follows exponential distribution with b.
0
$begingroup$
First, of all, forgive my English terminology. If you need any clarification let me know.
I do understand how E[X+Y] is calculated into E[X]+E[Y], but I'm having trouble when it is ^3.
Also, how can I find φ(x+y)(t)?
probability probability-theory probability-distributions
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
$endgroup$
add a comment |
0
$begingroup$
First, of all, forgive my English terminology. If you need any clarification let me know.
I do understand how E[X+Y] is calculated into E[X]+E[Y], but I'm having trouble when it is ^3.
Also, how can I find φ(x+y)(t)?
probability probability-theory probability-distributions
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
$endgroup$
1
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
1
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00
add a comment |
0
0
0
$begingroup$
First, of all, forgive my English terminology. If you need any clarification let me know.
I do understand how E[X+Y] is calculated into E[X]+E[Y], but I'm having trouble when it is ^3.
Also, how can I find φ(x+y)(t)?
probability probability-theory probability-distributions
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
$endgroup$
First, of all, forgive my English terminology. If you need any clarification let me know.
I do understand how E[X+Y] is calculated into E[X]+E[Y], but I'm having trouble when it is ^3.
Also, how can I find φ(x+y)(t)?
probability probability-theory probability-distributions
probability probability-theory probability-distributions
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
asked Jan 20 at 21:03
Nikos GavraNikos Gavra
11
11
1
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
1
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00
add a comment |
1
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
1
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00
1
1
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
1
1
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00
add a comment |
0
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1
$begingroup$
1. You haven't mentioned the dependence between $X$ and $Y$. (Are they independent?) 2. If they are independent, you can write $E[(X+Y)^3] = E[X^3] + 3 E[X^2] E[Y] + 3 E[X] E[Y^2] + E[Y^3]$ and compute each expectation individually. 3. Compute the expectation $phi_{X+Y}(t) = E[e^{i(X+Y) t}]$ directly.
$endgroup$
– angryavian
Jan 20 at 21:20
$begingroup$
Can you help me calculate E[X^3]? I'm not good with integrals.
$endgroup$
– Nikos Gavra
Jan 20 at 22:31
$begingroup$
Start with $int_0^infty x^3 a e^{-a x} , dx$ and do integration by parts three times. (Alternatively if you recognize the Gamma distribution you can avoid doing integration by parts.)
$endgroup$
– angryavian
Jan 20 at 22:34
$begingroup$
I did, but after the first integration by parts, I need to calculate [-x^3 * e^(-ax)] from 0 to oo, which if I'm not wrong, can't be calculated do to the oo. (forgive me again for the symbols I use, I'm not accustomed to it)
$endgroup$
– Nikos Gavra
Jan 20 at 22:39
1
$begingroup$
$lim_{x to infty} x^3 e^{-ax} = 0$. You should review how to compute $E[X]$ and $text{Var}(X)$ if you are uncomfortable with these computations.
$endgroup$
– angryavian
Jan 20 at 23:00