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95 percent confidence assigned assume average binomial distribution Brand Chebyshev's inequality chi-square chi-square distribution choose coin compute continuous type critical region defective defined discrete distribution function distribution with mean distribution with parameters error Example exponential distribution face value Figure Find the probability finite following results function F given Hence Hint histogram hypergeometric identically distributed independent random samples integer joint distribution large numbers law of large length Let Xlt Let Xx level confidence interval maximum likelihood estimate median negative binomial distribution null hypothesis observed outcome P-value percent confidence interval Poisson distribution population probability function Problems for Section proportion randomly selected rank reject H0 sample mean sample space Show standard deviation sufficient statistic Suppose Table test H0 Test the hypothesis Theorem tossed unbiased estimate uniform distribution variance a2 Xlt X2 zero elsewhere zero otherwise