Multinomial distribution

Multinomial distribution

1. Multinomial Distribution NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS https :// www.slideshare.net/NadeemUddin17 https ://nadeemstats.wordpress.com/listofbooks/

2. Multinomial experiment If each trial have more than two outcomes than the binomial experiment becomes a multinomial experiment . Multinomial distribution If a given trial can result in the k outcomes , with probability , then the probability distribution of the random variables , representing the number of occurrences for in “n” independent trials, is Where  

3. Example-1 An urn has 4 red, 6 blue and 5 green balls. A ball is randomly selected and then place back in the urn. Do this 5 times. What is the probability of choosing 1 red, 2 blue and 2 green balls? Solution    

5. Example-2 Throw a die 12 times. What is the probability that each face value (1, 2, 3, 4, 5, 6 ) will occur twice. Solution    

7. Example-3 Draw a card randomly from a deck of playing cards, with replacement, repeat this experiment 6 times. What is the probability of drawing 2 hearts, 2 diamonds, 1 spade and 1 clubs ? Solution  

9. Example-4 The probability that player A will win any game is 25%, the probability that player B will win is 25% and the probability that player C will win is 50%. If they play 10 games, what is the probability that player A will win 2 games, player B will win 3 games and player C will win 5 games? Solution