Mathematical Statistics

alternative hypothesis applies approximate assumes a value assumes the value average B₁ bility binomial distribution chi-square distribution coefficient coin committing a Type confidence interval criterion critical region degrees of freedom distribution function elements equal equation example Exercise exponential distribution F distribution Figure find the probability flips formula gamma distribution illustrate independent random variables integral joint density likelihood ratio mathematical mean method moment generating function n₁ n₂ normal population null hypothesis number of heads outcomes parameter Poisson distribution proba probability density probability distribution probability of committing probability of getting problems random sample random variables X1 refer regression represents the event sample space Section selected standard deviation standard normal distribution statistic subset suppose Table test the null tion Type II error value assumed value less variance verify want to test x₁ yields μ₁ σ²