Multinomial distribution: probability that at least one variable takes a certain value - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T23:11:54Z http://mathoverflow.net/feeds/question/90209 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90209/multinomial-distribution-probability-that-at-least-one-variable-takes-a-certain Multinomial distribution: probability that at least one variable takes a certain value madison54 2012-03-04T16:40:45Z 2012-03-04T16:40:45Z <p>Let $(X_1,\dots, X_M) \sim Mult(N;p_1,\dots,p_M)$ follow a multinomial distribution. What is the probability that <em>at least</em> one of the variables takes a certain value, i.e. $\mathbb{P}(\exists k\in \{1,\dots,M \}:X_k=n)$, where $n\in \{0,\dots,N\}$ is fixed?</p>