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Probability Distribution?

In this experiment you drop a marble down a board with a pyramid of nails. The marble the lands on a bin with bin 0 in the middle, bins 1 to 10 ranging to the right of zero, and bins -1 to -10 ranging to the left of 0. You drop the marble at the top of the board in alignment with bin 0.

Assume that you have twenty rows of nails and an infinite number of bins. You drop a marble from the center nail and let it go.

1.What is the probability of it falling into each bin? i.e. what is the real probability distribution?

2.Show that this distribution becomes a Gaussian distribution in some appropriate limit.

You basically have 20 independant trials with "success"=falling to the right of the nail and "failure" = falling to the left of the nail.

The number of "successes" is a binomial n=20, p=0.5. We must translate the outcome of this well-known random variable (let's call it X) into the ultimate position of the marble.

x=0 (all left) means the marbles lands at position -20.
x=1 (19 left and 1 right) marble lands at -18
x=2 → marble lands at -16
The general conversion is that the marble lands at position 2X-20. So for position Y=2X-20, the corresponding binomial value is X=(Y+20)/2.

1. p(y) = p(x=(y+20)/2)) where X~Binomial(0.5,20). Note that p(y)=0 if y is odd.

2. Y is a linear combination of a binomial variable, so by the Central Limit Theorem it will approximate a normal distribution with a large enough n.

PR Society Board Ten, Delegates One

No legislation was passed except for a minor loosening of rules for the international delegate and a resolution demanding the timely distribution of financials and the minutes of the preceding Assembly.Delegates did not get such documents until the day before or the day of the Assembly itself.

The PRS board bombarded the delegates throughout the Assembly with hundreds of slides, many of them with hundreds of words and complicated charts.

At least 90percent of the time was occupied by leader speeches or delegates doing “think tank” tasks at the direction of the leaders.

This was done to keep their attention off such real topics as decoupling APR from office holding; bringing back the printed directory; providing transcripts of the Assembly; moving the charter to Delaware to allow electronic meetings and votes; removing the three-year limit on Assembly service; ending proxy voting, and reporting assets the “normal” way (i.e., not booking 12 months of advance dues payments as immediate cash).

A round of applause greeted one speaker when he said he had no slides to show.

There were a few signs of rebellion/distrust among the delegates during the day.

One delegate got up and said the Assembly was being conducted “upside down,” meaning the delegates should be sitting on the stage and the board should be sitting below them.

This brought a round of applause and later in the meeting the directors came down from their perch and joined delegates who were seated at tables.

New Role for Assembly: Look Outside

Jean Frankel, of Tecker Consultants, Yardley, Pa., informed the delegates that the new trend in representative groups like the Assembly was for such groups to turn their attention outside and away from telling their boards of directors what to do.

The new role of the groups would be improving public acceptance of the entire profession, she said.

The PRS board would no doubt welcome such a development even though at present the Assembly has few powers over the board. Mostly what the Assembly does is elect the board and set dues.

The strategy of distraction and framing succeeded because the delegates, well over half of them serving for the first or second time, meekly accepted the incessant pitches and being turned into students of logical thinking by an outside consultant.

Although the stock market had just suffered one of its worst weeks ever and may have clipped $800,000 from the PRS treasury, the economy was barely mentioned.

The topic was especially germane in Detroit where the auto industry is under severe pressure and corridor talk was that General Motors and Chrysler would have to merge.

Chair Jeff Julin made the barest of mentions of what Newsweek has called an economic “nightmare.”

After noting that PRS tries to save up for a “rainy day,” Julin added: “It’s raining.”

Even accepting PRS’s unusual definition of “net assets,” it still has less than six months of cash on hand should its income plummet ($5.3M cash vs. expenses of about $12M).

Treasurer Rosanna Fiske was asked how much the $3.5M in “investments” had declined during the past few weeks but she would not provide a number.

he said PRS kept 60percent of the amount ($2.1M) in “equities,” 32-33percent in fixed income and 8percent in cash.

Chair-elect Mike Cherenson was asked what the “equities” consisted of but he had not replied as of press time. If PRS’s equities were hit with the nearly 40percent decline in stock prices in recent weeks, it would mean a paper loss in the area of $800,000.

The investment policy was set three years ago, Fiske said. A delegate wanted to know the size of the staff and was told it is 58. Twenty-five PRS staffers were listed in the advance roster of about 1,560 attendees.

Unlike previous years, the list of registrants was not distributed in the conference packets but was only available as a download.

Assembly delegates, about half of whom will not even be back next year, were given elaborate, time-consuming assignments on how to think about making bylaw and policy changes.

Hours were spent listening to presentations by Julin, COO Bill Murray, paid meetings consultant Frankel, Blake Lewis of the leadership task force, and executives of Ketchum who presented a survey on member satisfaction.

Lewis, who presented dozens of slides and said these were culled from a total of 263, said the group of 22 volunteers had concluded that there is “no clear, consistent path to leadership” in PRS and that a definition of leadership itself is needed.

One problem, he said, is keeping senior members involved in leadership.

PRS has a shortage of leaders, especially at the national level, partly because the APR requirement blocks 80percent of members from running for office. Requirements of heading a chapter, section, district or national committee or voting in an Assembly eliminate another 15percent or more of members.

Prof. Lynn Appelbaum of CCNY was recruited for Tri-State director this year after two deadlines for candidates had passed and no one showed up. The same thing happened to the Sunshine district this year. Last year there were difficulties in finding candidates from the Southeast and Southwest districts.

The PRS board, which would rather eliminate districts than allow non-APRs on the board, tried last year to shrink the districts from ten to five. But the Assembly defeated the bylaw change.

The tragedy of the 2008 Assembly, which wasted hours on pitches that should have been provided in advance, was that there was for the second year in a row no time for a “town hall.”

This was scheduled for one half hour (4:30-5 p.m.) at the end of a day that started at 7 a.m. for many delegates who attended various committee meetings. Some were jet-lagged by traveling from three time zones away.

As of mid-afternoon, the Assembly was running an hour behind schedule but full time was given to the “classes in thinking” by Frankel and the Lewis leadership presentation.

As of 4:25, the 2008 elections, which were supposed to have been passed by the Assembly more than a hour earlier, still had not been made.

Nominating chair Cheryl Procter-Rogers, apparently unmindful that this cut-and-dried formality (because there were no floor candidates) was cutting into time allotted for the town meeting, dragged out the nominations until 4:50 by giving many details of the nominating process.

What should have taken five minutes lasted more than 20 and by 4:53, two delegates came to the mike with resolutions that the minutes and financials be given to delegates in a timely fashion.

That about exhausted available time and Julin ruled the Assembly would end at 5 p.m. because that was in the agenda that was adopted.

Just over half of the delegates (almost all were still in the room) voted to continue but Julin noted that a two-thirds majority was needed to extend a meeting under Robert’s Rules.

What might have confused the delegates, who were talking among themselves, is that they had to vote “No” if they wanted the meeting to continue (i.e., over-rule the agenda), and “Yes” if they wanted to stick to the agenda and close the meeting.

The first vote was 52percent in favor of extending the meeting. To make sure delegates knew what they were doing, Julin then called for another vote. That came up 51percent in favor of the extension. Julin then ordered the meeting closed.

Delegates, who are duck soup for the association and legal experts who advise PRS leaders, should take a bigger role in preparing the agenda next year.

What they should do is simply not adjourn the meeting at all. Then they could meet whenever they want to by teleconference. Whatever they passed might not be legally binding but the national board would have to take notice.

About the Author

Jack O'Dwyer is publisher of www.odwyerpr.com, New York, and reports on behind the scenes organizations like PRSA and Entertainment Publicists Professional Society. He publishes a weekly newsletter and has been publishing directories of top PR firms for nearly four decades.

Distribution board fire

Distribution Board