4. A random variable X measuring the transfer time (in ms) between computers has a gamma distribution f(x; a, ß) with mean value u = 37.5 ms and standard deviation o = 21.6 ms. a) What are the values of the distribution parameters a and ß? b) What is the probability that the transfer time is between 50 and 75 ms? c) What is the 99'th percentile of the transfer time?

(8)(1)

4.52 Random variables X and Y follow a joint distribution f(x, y) = = 2, 0< x≤y< 1, otherwise. 0, Determine the correlation coefficient between X and Y.

A population of values has a normal distribution with μ=153.9μ=153.9 and σ=82.9σ=82.9. You intend to draw a random sample of size n=115n=115.A) Find P86, which is the score separating the bottom 86% scores from the top 14% scores. P86 (for single values) = B) Find P86, which is the mean separating the bottom 86% means from the top 14% means. P86 (for sample means) =