Let Y1, Y2, . . . , Yn be independent binomial random
Chapter 6, Problem 53E(choose chapter or problem)
Let \(Y_{1}, Y_{2} \ldots \ldots Y_{n}\) be independent binomial random variable with \(n_{i}\) trials and probability of success given by \(p_{i+} i=1,2, \ldots, n\)
a If all of the \(n_{i}\) 's are equal and all of the \(p\) 's are equal, find the distribution of
\(\sum_{i=1}^{n} Y_{i}\)
b If all of the \(n_{i}\) 's are different and all of the \(p^{*}\) 's are equal, find the distribution of \(\sum_{i=1}^{w} Y_{i}\).
c If all of the \(n_{i}\) 's are different and all of the \(p\) 's are equal, find the conditional distribution \(Y_{1}\) given \(\sum_{i=1}^{n} Y_{i}=m\) If all of the \(n_{i}\) 's are different and all of the \(p\) 's are equal, find the conditional distribution \(Y_{1}+Y_{1}\) given \(\sum_{j=1}^{*} Y_{i}=m\)
e If all of the \(p\) 's are different, does the method of moment-generating functions work well to find the distribution of \(\sum_{i=1}^{n} Y_{i}\)? Why?
Equation Transcription:
Text Transcription:
Y_1,Y_2......Y_n
n_i
p_i+i=1,2,...,n
ni
p
\sum i=_1^nY_1
n_i
p
\sum i=1^wY_1
n_i
p
Y1
\sum i=1^nY_1=m
n_i
p
Y1+Y1
\sum j=1Y_1=m
\sum i=1^nY_1
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