Mathematical Statistics

APPLIED EXERCISES approximation assign balanced coin Bernoulli distribution beta distribution binomial coefficients binomial distribution binomial probabilities chi-square distribution conditional probability corresponding critical region degrees of freedom denoted dice discrete distribution function elements equal equation estimate example find the probability flip following theorem formula gamma distribution given hence illustrate independent random variables instance integral joint density least marginal density mathematical Matterhorn ride mean moment generating function mutually exclusive events n₁ n₂ normal population null hypothesis number of different obtained parameter percent permutations points Poisson distribution positive integer possible outcomes prob probability function probability of getting prove Theorem random sample random variables x1 refer represents the event sample space Section standard deviation statistics subset substitution successes suppose test the null Theorem 1.7 THEORETICAL EXERCISES three shots tion total number tree diagram value less variance Venn diagram verify x₁