Vol. 7 No 5 - Pi Mu Epsilon

At&o boiMO.d by J. ANNULIS, JEANETTE BICKLEY, DAVID DELSESTO,
- ESSIG, MARK EVANS, JACK GARFUNKEL, ROBERT C. GEBHARDT, W. C.
IGIPS, RALPH KING, JEAN LANE, HENRY S. LIEBERMAN, JAMES A. PARSLY, BOB
PRIELIPP, TAGHI REZAY-GARACANI, SAHIB SINGH, ROBERT A. STUMP. PETER
SZABAGA, KENNETH M. WILKE, and the PROPOSER.
482. [Fa1 1 19801 Pkopode.d by Ronaid. E. Sk&ge~, Geo/wiA State.
UmMmiity.
Let X be a continuous random variable having a uniform distribution
with domain [a,b] and mean and standard deviation represented by p and
o, respectively. Verify that P( u - 20 5x2 p + 20) = 1
Solution by Bob P>u.eUpp, UnLunuLty of, WLficon^^-O&hkodh,
WLficonb-ui.
It is known that p = (a+b)/2 and 2 0 = (b-aI2/12 [see Table 4.1
on p. 83 of LINDGREN AND MCELRATH, Introduction to Probability and
Statistics, The Macmillan Co., New York, 19591. It follows that 2o =
(b-a)/&. Because u is the midpoint of [a,b], \X -p 1 5 (b-a)/2. But
6< 2 so 1/2 < 1/6 and hence (b-a)/2 < (b-a)//3. Therefore [X -p 1 <
(b-a)/fi = 20 so P( u- 2osXs \i + 20) = 1.
At20 4oLue.d by DANIEL ESSIG, MARK EVANS, ROBERT C. GEBHARDT, JOHN M.
HOWELL, W. C. IGIPS, HENRY S. LIEBERMAN, SAHIB SINGH, and the PROPOSER.
483. [Fall 19801 Pkopobed by PauJi Etdob, Spuce-~kip EMh.
Let u be the smallest integer for which p(p+ 1) = O(mod n).
n
mve 1