Poisson distribution with independent, identically distributed $X_i,$ )Cumulative distribution function or density for Compound Poisson distributionApproximate as Independent Identically distributedDeriving the distribution of poisson random variables.Determine the distribution of the sum of n independent identically distrubted poisson random variable $X_i$?Joint Distribution of n Poisson Random Variablesfunctions of identically distributed variables are identically distributedIndependent and identically distribued random variables $X_i$ with $X_1 sim exp(1/2)$independent Poisson-distribution random variableLimit of $S_N = sum_i=0^N X_i$ where $X_i$ is Laplace distributed and $N$ is Poisson distributed.Sum of Independent Poisson Distribution
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Poisson distribution with independent, identically distributed $X_i,$ )
Cumulative distribution function or density for Compound Poisson distributionApproximate as Independent Identically distributedDeriving the distribution of poisson random variables.Determine the distribution of the sum of n independent identically distrubted poisson random variable $X_i$?Joint Distribution of n Poisson Random Variablesfunctions of identically distributed variables are identically distributedIndependent and identically distribued random variables $X_i$ with $X_1 sim exp(1/2)$independent Poisson-distribution random variableLimit of $S_N = sum_i=0^N X_i$ where $X_i$ is Laplace distributed and $N$ is Poisson distributed.Sum of Independent Poisson Distribution
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How can I find E($tildeX$) and Var($tildeX$) of a Poisson distribution with independent, identically distributed $X_i,$ )
probability poisson-distribution
asked Mar 29 at 3:22
NathanNathan
54
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$begingroup$
How can I find E($tildeX$) and Var($tildeX$) of a Poisson distribution with independent, identically distributed $X_i,$ )
probability poisson-distribution
asked Mar 29 at 3:22
NathanNathan
54
$endgroup$
add a comment |
$begingroup$
How can I find E($tildeX$) and Var($tildeX$) of a Poisson distribution with independent, identically distributed $X_i,$ )
probability poisson-distribution
asked Mar 29 at 3:22
NathanNathan
54
$endgroup$
How can I find E($tildeX$) and Var($tildeX$) of a Poisson distribution with independent, identically distributed $X_i,$ )
probability poisson-distribution
probability poisson-distribution
asked Mar 29 at 3:22
NathanNathan
54
asked Mar 29 at 3:22
NathanNathan
54
edited Mar 31 at 1:42
Nathan
asked Mar 29 at 3:22
NathanNathan
54
asked Mar 29 at 3:22
NathanNathan
54
asked Mar 29 at 3:22
NathanNathan
54
54
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2 Answers
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You still need the sum signs in the last step there; it should be $frac1nleft(sum_i=1^n E(X_i)right)$ and $frac1n^2left(sum_i=1^n V(X_i)right)$.
How can I finish it for $X_i$ iid Poisson($lambda$)?
What is the mean of a Poisson distribution with parameter $lambda$? The variance? Then we add up $n$ copies of that, and divide by $n$ or $n^2$.
answered Mar 29 at 3:38
jmerryjmerry
17k11633
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I assume $tilde X$ is the same as $bar X$...
a) You are almost there but $E sum_i x_i = n E X$ given $X$ is i.i.d, hence the first answer $E bar X = E X$.
b) ditto here: $V sum_i X_i = n V X$ if $X$ is i.i.d., and hence the answer is $frac1n V X$.
Note that it depends on the i.i.d assumption, but not on the Poisson distribiton.
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
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2 Answers
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2 Answers
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$begingroup$
You still need the sum signs in the last step there; it should be $frac1nleft(sum_i=1^n E(X_i)right)$ and $frac1n^2left(sum_i=1^n V(X_i)right)$.
How can I finish it for $X_i$ iid Poisson($lambda$)?
What is the mean of a Poisson distribution with parameter $lambda$? The variance? Then we add up $n$ copies of that, and divide by $n$ or $n^2$.
answered Mar 29 at 3:38
jmerryjmerry
17k11633
$endgroup$
add a comment |
$begingroup$
You still need the sum signs in the last step there; it should be $frac1nleft(sum_i=1^n E(X_i)right)$ and $frac1n^2left(sum_i=1^n V(X_i)right)$.
How can I finish it for $X_i$ iid Poisson($lambda$)?
What is the mean of a Poisson distribution with parameter $lambda$? The variance? Then we add up $n$ copies of that, and divide by $n$ or $n^2$.
answered Mar 29 at 3:38
jmerryjmerry
17k11633
$endgroup$
add a comment |
$begingroup$
You still need the sum signs in the last step there; it should be $frac1nleft(sum_i=1^n E(X_i)right)$ and $frac1n^2left(sum_i=1^n V(X_i)right)$.
How can I finish it for $X_i$ iid Poisson($lambda$)?
What is the mean of a Poisson distribution with parameter $lambda$? The variance? Then we add up $n$ copies of that, and divide by $n$ or $n^2$.
answered Mar 29 at 3:38
jmerryjmerry
17k11633
$endgroup$
You still need the sum signs in the last step there; it should be $frac1nleft(sum_i=1^n E(X_i)right)$ and $frac1n^2left(sum_i=1^n V(X_i)right)$.
How can I finish it for $X_i$ iid Poisson($lambda$)?
What is the mean of a Poisson distribution with parameter $lambda$? The variance? Then we add up $n$ copies of that, and divide by $n$ or $n^2$.
answered Mar 29 at 3:38
jmerryjmerry
17k11633
answered Mar 29 at 3:38
jmerryjmerry
17k11633
answered Mar 29 at 3:38
jmerryjmerry
17k11633
answered Mar 29 at 3:38
jmerryjmerry
17k11633
17k11633
add a comment |
add a comment |
$begingroup$
I assume $tilde X$ is the same as $bar X$...
a) You are almost there but $E sum_i x_i = n E X$ given $X$ is i.i.d, hence the first answer $E bar X = E X$.
b) ditto here: $V sum_i X_i = n V X$ if $X$ is i.i.d., and hence the answer is $frac1n V X$.
Note that it depends on the i.i.d assumption, but not on the Poisson distribiton.
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
$endgroup$
add a comment |
$begingroup$
I assume $tilde X$ is the same as $bar X$...
a) You are almost there but $E sum_i x_i = n E X$ given $X$ is i.i.d, hence the first answer $E bar X = E X$.
b) ditto here: $V sum_i X_i = n V X$ if $X$ is i.i.d., and hence the answer is $frac1n V X$.
Note that it depends on the i.i.d assumption, but not on the Poisson distribiton.
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
$endgroup$
add a comment |
$begingroup$
I assume $tilde X$ is the same as $bar X$...
a) You are almost there but $E sum_i x_i = n E X$ given $X$ is i.i.d, hence the first answer $E bar X = E X$.
b) ditto here: $V sum_i X_i = n V X$ if $X$ is i.i.d., and hence the answer is $frac1n V X$.
Note that it depends on the i.i.d assumption, but not on the Poisson distribiton.
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
$endgroup$
I assume $tilde X$ is the same as $bar X$...
a) You are almost there but $E sum_i x_i = n E X$ given $X$ is i.i.d, hence the first answer $E bar X = E X$.
b) ditto here: $V sum_i X_i = n V X$ if $X$ is i.i.d., and hence the answer is $frac1n V X$.
Note that it depends on the i.i.d assumption, but not on the Poisson distribiton.
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
answered Mar 29 at 3:41
Ott ToometOtt Toomet
1114
1114
add a comment |
add a comment |
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