## Applications of Probability and Random VariablesProbability concepts; Discrete Random variables; Probability and difference equations; Continuous Random variables; Joint distributions; Derived distributions; Mathematical expectation; Generating functions; Markov processes and waiting lines; Some statistical uses of probability. |

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acceptance region admissible region admissible values applied arbitrary assume binomial distribution chi-square coefficients computed conditional distribution conditional probability consider constant corresponding critical region curve defined definition degrees of freedom denote derived determine deviation difference equation discrete variate distribution function equal estimate event EXAMPLE expected value exponential FIGURE find the distribution finite follows function f(x gamma distribution given Hence integral interval joint density function joint distribution level of significance linear marginal distribution Markov process mathematical matrix moment-generating function mutually exclusive normal distribution null hypothesis obtain occur pair parameters Poisson distribution population prob probability density profit random sample random variable range relative frequency respectively ri ri ri roots sample value solution square statistic substitution Suggested Problems Table test variate Theorem tion total probability unity whence xu x2 yield zero