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(a) In hypothesis testing, the type-II error is the probability of not rejecting the null hypothesis when the alternative is true. (b) Suppose X has cdf F(x) and Y has cdf G(y) = F(y ). If we have < 0, it means Y population is located at the left of X population.

(c) Any marginal distribution of a multinomial distribution is is another multinomial distribution.

(d) To test simple hypotheses, the Bayes factor is the likelihood ratio.

(e) A few poisson distributed random variables with fixed sum can be considered to have a multinomial distribution involving the parameters of the poisson distributions.