## Sunday, March 31, 2019

### HP 17BII: Normal Distribution and Random Number Generators

HP 17BII:  Normal Distribution and Random Number Generators

Normal Distribution

The following solver approximates the area of a normal distribution.  The following equation uses L (Let) and G (Get), so this can be used for the classic HP 17BII and the silver HP 17BII+.

NORM: CDF=1-EXP(-X^2÷2)÷SQRT(2*PI)*(.4361836*
L(T:INV(1+.33267*X))-.1201676*G(T)^2+.9372980*G(T)^3)

Instructions:

For x ≥ 0, enter x in ( X ) and then press (CDF) to solve.

For x < 0, enter abs(x) in ( X ), press (CDF) to solve, negate the result and add 1.

The area will be calculated from 0 (the center) to x.

Example 1:  x = 2.5

2.5 (X), (CDF):  Result:  0.99

Example 2:  x = 1

1 (X), (CDF):  Result: 0.84

Example 3:  x = -1.5

(Algebric Mode)

1.5 (X), (CDF) [+/-] [ + ] 1 [ = ]:  Result:  0.07

Source:

"Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphics, Transforms"  Research & Education Association.  1984  ISBN 0-87891-521-4

Random Numbers

The HP 17B series does not have a random number function.  We can use the solver to generate random numbers.  Random numbers between 0 to 1 are generator.

The format to use will depend on the version of HP 17B you are working with.

The code used will use pseudo-random generator:

r_i+1 = frac( ( π + r_i)^5 )

Classic HP 17B and HP 17BII:

We can use Let and Get to generate random numbers, they are used to generate in recurring sequences.

R#=FP((PI+G(R#))^5)

Instructions:

Enter a starting seed, press (R#).
For future random numbers, keep on pressing (R#).

Brown and Silver HP 17BII+:

We'll use the two variables.  Despite the fact that Let and Get are available on the silver HP 17BII+, they cannot be used in recurring sequences.

R2#=FP((PI+R1#)^5)

Instructions:
Enter a starting seed, press (R1#).
For the first random number, press (R2#).
For future random numbers, press [ STO ] (R1#), then (R2#).

Other pseudo-random number generators to try:

r_i+1 = frac( 997 * r_i )

r_i+1 = frac( 147 * r_i )

Eddie

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