Show that the parameters of the beta distribution can be expressed as follows in terms of the mean and the variance of this distribution:
Answer to relevant QuestionsIf a random variable X has a uniform density with the parameters a and β, find its distribution function. In the proof of Theorem 6.6 we twice differentiated the moment– generating function of the normal distribution with respect to t to show that E(X) = µ and var(X) = σ2. Differentiating twice more and using the formula of ...Show that if X is a random variable having the Poisson distribution with the parameter λ and λ → ∞, then the moment-generating function of Z = X – λ / √λ That is, that of a standardized Poisson random variable, ...In certain experiments, the error made in determining the density of a substance is a random variable having a uniform density with α = – 0.015 and β = 0.015. Find the probabilities that such an error will (a) Be ...A certain kind of appliance requires repairs on the average once every 2 years. Assuming that the times between repairs are exponentially distributed, what is the probability that such an appliance will work at least 3 years ...
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