Question: Show that the parameters of the beta distribution can be
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 ...
Post your question