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autobot.d
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What kind of problem is this?
[itex] X_i \textrm{are iid with known mean and variance, } \mu \textrm{ and } \sigma ^2 \textrm{respectively. }[/itex]
[itex] m \sim \textrm{Binomial(n,p), n is known.}[/itex]
[itex]S = \sum^{m}_{i=1} X_i[/itex]
How do I work with this? This what I have thought of.
[itex]S = \sum^{m}_{i=1} X_i = mX_1 \textrm{(since iid)}[/itex]
so for the mean of S
[itex] \bar{S} = \bar{mX_i} = np \mu ? [/itex]
or to find mean of S use expected value
[itex] E(S) = E(mX_i) = E(mX_1) \textrm{ (since iid)} [/itex]
but then what?
Any help would be appreciated. I am guessing this kind of problem has a name?
Thanks.
[itex] X_i \textrm{are iid with known mean and variance, } \mu \textrm{ and } \sigma ^2 \textrm{respectively. }[/itex]
[itex] m \sim \textrm{Binomial(n,p), n is known.}[/itex]
[itex]S = \sum^{m}_{i=1} X_i[/itex]
How do I work with this? This what I have thought of.
[itex]S = \sum^{m}_{i=1} X_i = mX_1 \textrm{(since iid)}[/itex]
so for the mean of S
[itex] \bar{S} = \bar{mX_i} = np \mu ? [/itex]
or to find mean of S use expected value
[itex] E(S) = E(mX_i) = E(mX_1) \textrm{ (since iid)} [/itex]
but then what?
Any help would be appreciated. I am guessing this kind of problem has a name?
Thanks.