fa(^; a, ß) = r(x) where a and ß are parameters of the distribution, and r(·) is the Gamma function (see Lecture 1 if don't remember what this function is), with derivative denoted by r'(-). Show that it is a conjugate prior of Poisson (A), i.e., when the observations X; for 1

Explain why this statement is true: Suppose you take large repeated samples of a variable X (which is uniformly distributed). The distribution of the sample means will also be uniform. 

How does the shape of a t-distribution compare with the normal distribution? How does the shape of a t-distribution depend on sample size?

How would I work this problem out? Thanks

Scores on an TOFEL for IT school candidates are normally distributed with μ = 140 and s = 14 What is the probability a candidate will likely score above 160? What percentage of candidates will likely score below 140?

The first pic is the question. Since some tutors have been solving the problems wrong recently (no judgment), I’ve added a sample question to solve problem.

I need help with question and show step by step solution