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Let X1, ..., Xn be i.i.d. random variables from P(a,θ), where (a, θ) ∈ R2 is a parameter. Find a two-dimensional sufficient statistic for (a, θ) in the following cases.
(a) P(a,θ) is the exponential distribution E(a, θ), a ∈ R, θ ∈ (0, ∞).
(b) P(a,θ) is the Pareto distribution Pa(a, θ), a ∈ (0, ∞), θ ∈ (0, ∞).
Each F-distribution is identified by two numbers of degrees of freedom, one for each of the two samples involved.
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a normally distributed quality characteristic is monitored throughuse of an x bar and r chart. these charts have the
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1. A fair die is rolled 12 times. Given that there are exactly two ones, what is the probability that there are exactly two sixes? 2. A fair die is rolled twice. Compute the probability that the sum of the two rolls is 3, 5, 7, 9, 11, respectively,..
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