Advanced BASIC Scientific Subroutines by B.V. Cordingley, D.J. Chamund

By B.V. Cordingley, D.J. Chamund

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8491 found by simulation (see subroutine RNDPSN). 8481. The discrepancy is well within the expected precision of the process of simulation. The Subroutines 25 AREA UNDER THE NORMAL CURVE Subroutine: NORMDT Description Computes the area under the upper and lower tails of the standard normal curve. 28 = (1/21T'fl exp(-z2/2)f(z) This technique is based on the work published by Adams (Adams, 1969) and subsequently adapted and published in Applied Statistics Algorithms (Griffiths and Hill, 1985a). •....

The upper tail probability for t is determined directly from the subroutine BETAFN rather than via the subroutine FDISTN and is set equal tolx (P,q)/2 (see notes on BETAFN). ,2)2/2) for X. Subroutine Listing 4000 4010 4020 4030 4040 4050 4060 4070 4080 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190 4200 4210 4220 4230 4240 4250 4260 REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM AREA UNDER STUDENT'S T DISTRIBUTION SUBROUTINE: TDISTR COMPUTES THE AREA UNDER THE UPPER TAIL OF CENTRAL T-DISTRIBUTION FOR OF DEGREES OF FREEDOM FROM XT TO INFINITY.

NUMBER OF SUCCESSES PB ...... PROB. OF SUCCESS ON A SINGLE TRIAL OUTPUT: FX ...... PROB. OF NUMSUC OR FEWER SUCCESSES PX ...... PROB. OF EXACTLY NUMSUC SUCCESSES LOCAL: ... R, OB The Subroutines 2170 2180 2190 2200 2210 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 REM REM 21 CHECK INPUT DATA IF PB < 0 OR PB > 1 OR NB < 1 THEN GOTO 2310 IF NUMSUC > NB OR NUMSUC < 0 THEN GOTO 2310 LET QB 1 - PB LET PX = QB~NB LET FX = PX IF NUMSUC = 0 THEN GOTO 2290 FOR R = 1 TO NUMSUC LET PX (NB + 1 - R)*PB*PX/(R*QB) LET FX = FX + PX NEXT R REM RETURN REM PRINT " PB, NB OR NUMSUC INVALID" PRINT" PB = "; PB; ", NB = "; NB; PRINT ", NUMSUC = "; NUMSUC END Sample Program If five dice are thrown, determine (a) the probability that exactly three sixes are thrown and (b) the probability of throwing three or more sixes.

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