Show that $e^{-mu+frac{sigma^2}{2}} $ is estimable if $frac{mu}{sigma}$ is estimable.
$begingroup$
Suppose $X_1,X_2,...,X_n sim^{i.i.d} N(mu,sigma^2)$.Show that $e^{-mu+frac{sigma^2}{2}} $ is estimable if $frac{mu}{sigma}$ is estimable.
I am utterly confused, in fact I can think of this as two problems combined that is I know, $E(frac{sum e^{-X_i}}{n})=e^{-mu +frac{sigma^2}{2}}$ and also, I can estimate $frac{mu}{sigma}$ by $Cfrac{bar{X}}{S}$ where $C$ is a known constant.But where can I connect between the two?
Am I using any assumptions here so that I can estimate either of them?
Help!
probability probability-theory probability-distributions normal-distribution parameter-estimation
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
$endgroup$
add a comment |
$begingroup$
Suppose $X_1,X_2,...,X_n sim^{i.i.d} N(mu,sigma^2)$.Show that $e^{-mu+frac{sigma^2}{2}} $ is estimable if $frac{mu}{sigma}$ is estimable.
I am utterly confused, in fact I can think of this as two problems combined that is I know, $E(frac{sum e^{-X_i}}{n})=e^{-mu +frac{sigma^2}{2}}$ and also, I can estimate $frac{mu}{sigma}$ by $Cfrac{bar{X}}{S}$ where $C$ is a known constant.But where can I connect between the two?
Am I using any assumptions here so that I can estimate either of them?
Help!
probability probability-theory probability-distributions normal-distribution parameter-estimation
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
$endgroup$
add a comment |
$begingroup$
Suppose $X_1,X_2,...,X_n sim^{i.i.d} N(mu,sigma^2)$.Show that $e^{-mu+frac{sigma^2}{2}} $ is estimable if $frac{mu}{sigma}$ is estimable.
I am utterly confused, in fact I can think of this as two problems combined that is I know, $E(frac{sum e^{-X_i}}{n})=e^{-mu +frac{sigma^2}{2}}$ and also, I can estimate $frac{mu}{sigma}$ by $Cfrac{bar{X}}{S}$ where $C$ is a known constant.But where can I connect between the two?
Am I using any assumptions here so that I can estimate either of them?
Help!
probability probability-theory probability-distributions normal-distribution parameter-estimation
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
$endgroup$
Suppose $X_1,X_2,...,X_n sim^{i.i.d} N(mu,sigma^2)$.Show that $e^{-mu+frac{sigma^2}{2}} $ is estimable if $frac{mu}{sigma}$ is estimable.
I am utterly confused, in fact I can think of this as two problems combined that is I know, $E(frac{sum e^{-X_i}}{n})=e^{-mu +frac{sigma^2}{2}}$ and also, I can estimate $frac{mu}{sigma}$ by $Cfrac{bar{X}}{S}$ where $C$ is a known constant.But where can I connect between the two?
Am I using any assumptions here so that I can estimate either of them?
Help!
probability probability-theory probability-distributions normal-distribution parameter-estimation
probability probability-theory probability-distributions normal-distribution parameter-estimation
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
edited Jan 23 at 16:05
Legend Killer
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
asked Jan 23 at 15:51
Legend KillerLegend Killer
1,6671524
1,6671524
add a comment |
add a comment |
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