Problem 15E

Given a fair four-sided die, let Y equal the number of rolls needed to observe each face at least once.

(a) Argue that Y = X1 + X2 + X3 + X4, where Xi has a geometric distribution with pi = (5−i)/4, i = 1, 2, 3, 4, and X1,X2,X3,X4 are independent.

(b) Find the mean and variance of Y.

(c) Find P(Y = y), y = 4, 5, 6, 7.

Section 3.4 & 3.5 David Holmes STAT 250 Feb 22 Comparing Measures and Distributions Appropriate Measures Using Measures to Determine Shape Using Measures to Compare Distributions Appropriate Measures When dealing with numerical data, one describes the distribution using the characteristics: shape, center, and spread. • What measures for center and spread is best suited for the data Mean or median Standard deviation or IQR • Depends on the shape of the distribution! The shape of the distribution will determine which measures are best for communicating typical values and variability. Example 3.14: S