Multinomial Distribution Concepts

The video tutorial introduces the multinomial distribution as a generalization of the binomial distribution, allowing for more than two outcomes per trial. It provides examples, including blood type distribution in the U.S. and an urn problem, to illustrate how to calculate probabilities using the multinomial distribution. The tutorial also explains the difference between sampling with and without replacement, introducing the multivariate hypergeometric distribution for the latter scenario.

What is the multinomial distribution a generalization of?

• Exponential distribution

• Normal distribution

• Poisson distribution

• Binomial distribution

In the multinomial distribution, how many possible outcomes can there be on a single trial?

• At least 4

• Exactly 3

• More than 2

• Only 2

What is the probability of 6 people having blood type O in a sample of 10 Americans?

• 0.01290

• 0.18204

• 0.044

• 0.13122

What must the sum of probabilities for all outcomes in a multinomial distribution equal?

• k

• n

• 1

• 0

What does the random variable X_i represent in the multinomial distribution?

• The mean of outcome i

• The variance of outcome i

• The number of occurrences of outcome i

• The probability of outcome i

What is the expectation of X_i in a multinomial distribution?

• p_i / n

• n * p_i

• n - p_i

• n + p_i

In the blood type example, what is the probability of blood type A occurring twice?

• 0.10

• 0.04

• 0.44

• 0.42

What is the significance of 'with replacement' in the ball example?

• It makes trials dependent

• It alters the total number of balls

• It changes the number of trials

• It keeps trials independent

What is the probability of drawing 2 red balls in the ball example?

• 0.044

• 0.18204

• 0.01290

• 0.13122

What distribution is used when sampling without replacement?

• Binomial distribution

• Multivariate hypergeometric distribution

• Normal distribution

• Multinomial distribution