Questions and Answers of Bayesian Statistics An Introduction

The skewness of a random variable x is defined as y1 = µ3/(µ,2) 3/2 where
Suppose that a continuous random variable X has meanµ, and variance ϕ. By writing and using a lower bound for the integrand in the latter integral, prove that Show that the result also holds for
Suppose that x and y are such that Show that x and y are uncorrelated but that they are not independent. P(x = 0, y = 1) = P(x = 0, y = − 1) = P(x = 1, y = 0) = P(x = -1, y = 0) = 1.
Let x and y have a bivariate normal distribution and suppose that x and y both have mean 0 and variance 1, so that their marginal distributions arc standard normal and their joint density is Show
Suppose that x has a Poisson distribution (see question 6) P(λ) of mean λ and that, for given x, y has a binomial distribution B(x,π) of index x and parameter π.(a) Show that the unconditional
Define and show (by setting z = xy and then substituting z for y) thatDeduce that By substituting (I + x2)z2 = 2t, so that z dz = dt /(1 + x2) show that I = √π/2, so that the density of the

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