If Y1,Y2,Y2 ~ Multinomial with parameter (n,p1,p2,p3)(adsbygoogle = window.adsbygoogle || []).push({});

Prove that the conditional distribution of Y1 given Y3=m (m<n)

is a binomial with ( (n-m), p1/(p1+p2) )

p1+p2+p3=1

y1+y2+y3=n

y3=m

My Attempt:

P( Y1=y1| y3=m) = P(Y1=y1, Y3=m)/ P(Y3=m)

( n choose m and y1 ) p1^y1*p3^m / ( n choose m) p3^m*(p1+p2)^n-m

leaving me with

(n-m)!/ y1! (p1/ p1+p2)^y1((p1+p2) ^y2))

....

can't seem to simplyfy this to become a binomial

honestly stuck here!

Thanks!

**Physics Forums - The Fusion of Science and Community**

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

# Conditional Multinomial Problem

Loading...

Similar Threads - Conditional Multinomial Problem | Date |
---|---|

A Value at Risk, Conditional Value at Risk, expected shortfall | Mar 9, 2018 |

I Equality in conditional probability | Jan 18, 2018 |

I Rewriting of equality in conditional probability distribution | Jan 16, 2018 |

B Conditional Probability, Independence, and Dependence | Dec 29, 2017 |

Conditional Epectation of Multinomial | Dec 10, 2014 |

**Physics Forums - The Fusion of Science and Community**