If X and Y are binomial random variables with respective parameters (n,p) and (n,1-p), verify and explain the following identities:(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Verify and Explain Binomial R.V. Identities

**Physics Forums | Science Articles, Homework Help, Discussion**