Question

X denote the mean of a random sample of size 25 from a gamma type distribu- tion with a = 4 and β > 0. Use the Central Limit theorem to find an approximate 0.954 confidence interval for μ, the mean of the gallina distribution. Hint: Use the random variable (X-43)/?7,/432/25. 6. Let Yi < ½ < < }, denote the order statistics of a randon sample of size n from a distribution that has pdf f(z) = 4r3/04, O <エ< θ, zero elsewhere. (a) Show that P(c < y./θ < 1) = 1-e*n 1. (b) If n is 5 and if the observed value of Y, is 2.4, what is a 95% confidence interval where 0<e< for θ?
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