Statistics - Multinomial Distribution

Statistics – Multinomial Distribution

A multinomial experiment is a statistical experiment and it consists of n repeated trials. Every trial has a discrete variety of potential outcomes. On any given trial, the chance {that a} specific end result will happen is fixed.

Method

Pr=n!(n1!)(n2!)...(nx!)P1n1P2n2...PxnxPr=n!(n1!)(n2!)…(nx!)P1n1P2n2…Pxnx

The place −

  • nn = variety of occasions
  • n1n1 = variety of outcomes, occasion 1
  • n2n2 = variety of outcomes, occasion 2
  • nxnx = variety of outcomes, occasion x
  • P1P1 = chance that occasion 1 occurs
  • P2P2 = chance that occasion 2 occurs
  • PxPx = chance that occasion x occurs

Instance

Downside Assertion:

Three card gamers play a collection of matches. The chance that participant A will win any recreation is 20%, the chance that participant B will win is 30%, and the chance participant C will win is 50%. In the event that they play 6 video games, what’s the chance that participant A will win 1 recreation, participant B will win 2 video games, and participant C will win 3?

Answer:

Given:

  • nn = 12 (6 video games complete)
  • n1n1 = 1 (Participant A wins)
  • n2n2 = 2 (Participant B wins)
  • n3n3 = 3 (Participant C wins)
  • P1P1 = 0.20 (chance that Participant A wins)
  • P1P1 = 0.30 (chance that Participant B wins)
  • P1P1 = 0.50 (chance that Participant C wins)

Placing the values into the formulation, we get:

Pr=n!(n1!)(n2!)...(nx!)P1n1P2n2...Pxnx, Pr(A=1,B=2,C=3)=6!1!2!3!(0.21)(0.32)(0.53), =0.135