- #1
knowLittle
- 312
- 3
If X and Y are binomial random variables with respective parameters (n,p) and (n,1-p), verify and explain the following identities:
a.) P{X<=i}= P{Y>=n-i};
b.) P{X=k}= P{Y=n-k}
Relevant Equations:
P{X=i}=nCi *p^(i) *(1-p)^(n-i), where nCi is the combination of "i" picks given "n".
Distribution function
##p\left\{ x\leq i\right\} =\sum _{k=0}^{i}\left( n_{k}\right) p^{k}\left( 1-p\right) ^{n-k}
##, where n_k is ## (_{k}^{n})
##
Solution:
I don't know, how to start the problem. Please, help.
a.) P{X<=i}= P{Y>=n-i};
b.) P{X=k}= P{Y=n-k}
Relevant Equations:
P{X=i}=nCi *p^(i) *(1-p)^(n-i), where nCi is the combination of "i" picks given "n".
Distribution function
##p\left\{ x\leq i\right\} =\sum _{k=0}^{i}\left( n_{k}\right) p^{k}\left( 1-p\right) ^{n-k}
##, where n_k is ## (_{k}^{n})
##
Solution:
I don't know, how to start the problem. Please, help.