Consider a random sample of size n from a continuous distribution having median 0 so that the

Question:

Consider a random sample of size n from a continuous distribution having median 0 so that the probability of any one observation being positive is .5. Disregarding the signs of the observations, rank them from smallest to largest in absolute value, and let W = the sum of the ranks of the observations having positive signs. For example, if the observations are -.3, + .7, + 2.1, and - 2.=, then the ranks of positive observations are 2 and 3, so W = 5. In Chapter 1=, W will be called Wilcoxon's signed-rank statistic. W can be represented as follows:
w = 1. Y, + 2· Y, + 3 · Y, + · . - + n -Σi.Υ. · Y, i-1

where the Yi's are independent Bernoulli rv's, each with p = .5 (Yi = 1 corresponds to the observation with rank i being positive).
a. Determine E(Yi) and then E(W) using the equation for W.
b. Determine V(Yi) and then V(W).

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
Fantastic news! We've located the answer you've been seeking!

Step by Step Answer:

Question Posted: