Let x1, . . . , xn iid from N(µ, σ^2 ) where σ^2 = 1. (a) Show that the Jeffreys prior for the normal likelihood is p(µ) = c1 √n/σ^2 , µ ∈ R for some constant c1 > 0. (b) Is this a proper prior or improrer prior? Explain.

Let X be a continuous random variable with a pdf given by f(x) = (3x^2)/2 where x lies in the closed interval [-1,1]. Evaluate P(x>1/2). Select the correct response: 7/16 8/17 2/17 7/8

The joint probability distribution of the random variables is f(x,y)= 8xy, 0<=y<=x<=1. fine the covarience of x and y

The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem  to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.