The Multinomial Distribution

Several categories at once

Marginals by lumping

Conditioning one count

In 4 independent trials with category probabilities 0.5, 0.3, 0.2, what is P(counts are exactly 2, 1, 1)?

X is Mult_3(20, 0.2, 0.5, 0.3). What is the distribution of X_2 alone?

Trials fall in four categories with probabilities 0.1, 0.2, 0.3, 0.4. You lump the first two categories together. The lumped count over 15 trials is Binomial(15, p). What is p? Enter a decimal like 0.3.

For Mult_k(n, p) with n = 40, p_1 = 0.25 and p_2 = 0.15, Cov(X_1, X_2) equals minus n p_1 p_2. Compute the value. Enter like -1.5.

Mult_3(12, 0.5, 0.3, 0.2) is conditioned on X_1 = 7. The remaining counts (X_2, X_3) form a Mult_2 with how many trials, and with what probability on category 2? Give n as an integer.

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.