### Table 30.1 gives a number of common probability density functions and corresponding characteristic functions, means, and variances. Further information may be found in Refs. [1{ 8] and [10]; Ref. [10] has particularly detailed tables. Monte Carlo techniques for generating each of them may be found in our Sec. 32.4. We comment below on all except the trivial uniform distribution. 30.4.1. Binomial distribution: A random process with exactly two possible outcomes which occur with xed probabilities is called a Bernoulli process. If the probability of obtaining a certain outcome (a \success quot;) in each trail is p, then the probability of obtaining exactly r successes (r =0;1;2;:::;N)inNindependent trials, without regard to the order of the successes and failures, is given by the binomial distribution f(r; N;p) in Table 30.1. If r and s are binomially distributed with parameters (Nr;p)and(Ns;p), then t = r + s follows a binomial distribution with parameters (Nr + Ns;p).

### Table 1: Inference permutability in MALL2

"... In PAGE 4: ... The results that conclude this study can be easily transposed to second order linear logic. Here, we are only interested in the fragment MALL2 for which inference permutabil- ity can be summarised in Table1 . There are eight cases of non permutability cor- responding to the eight entries of the table that are marked by np 1.... ..."

### Table 1: Error introduced by normal approximations

1993

"... In PAGE 6: ... Second, the probabili- ties computed using the normal approximation are less and less accurate. Table1 shows the probability that one or more matches are found in 100 words of text as computed using the binomial and normal distributions for np = 0.... In PAGE 7: ... Table1 shows that for rare events, the normal distribution does not even approximate the bino- mial distribution. In fact, for np = 0.... ..."

Cited by 501

### Table 1: Error introduced by normal approximations

1993

"... In PAGE 6: ... Second, the probabili- ties computed using the normal approximation are less and less accurate. Table1 shows the probability that one or more matches are found in 100 words of text as computed using the binomial and normal distributions for np = 0.... In PAGE 7: ... Table1 shows that for rare events, the normal distribution does not even approximate the bino- mial distribution. In fact, for np = 0.... ..."

Cited by 501

### Tables of the Binomial Probability Distribution, National

1972