Wednesday, August 31, 2016

HP 12C: Combination/Binomial Distribution/Negative Binomial Distribution



HP 12C:  Combination/Binomial Distribution/Negative Binomial Distribution

Introduction and Formulas

Combination: Find the number of groups out of a possible set of objects.  The order of objects obtained does not matter. 
Store n in R1, x in R0, and p in R2.  Press [ f ] [ R↓]  (CLEAR PRGM), [ R/S ]
Formula:  COMB(n, x)  = n!/(x! * (n-x)!)

Binomial Distribution:  Find number of successes (x) in a fixed number of trials (n). 
Store n in R1, x in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 26, [R/S]
Formula:  COMB(n, x) * p^x * (1 – p)^(n – x)

Negative Binomial Distribution:  Find the number of trials (n) needed to obtain a fixed amount of successes (x).
Store x in R1, n in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 43, [R/S]
Formula:  COMB(x – 1, n – 1) * p^(n -1) * (1 – p)^((x - 1) - (n – 1))

In the distribution calculations, p is the probability where 0 ≤ p ≤ 1. 
Note: R3 is used as a flag, which will allowed for branching.

STEP
CODE
KEY
Combination


01
0
0
02
44, 3
STO 3
03
45, 1
RCL 1
04
43, 3
N!
05
45, 0
RCL 0
06
43, 3
N!
07
10
÷
08
45, 1
RCL 1
09
45, 0
RCL 0
10
30
-
11
43, 3
N!
12
10
÷
Flag Testing


13
45, 3
RCL 3
14
1
1
15
30
-
16
43, 35
X=0
17
43, 33, 29
GTO 29
18
45, 3
RCL 3
19
2
2
20
30
-
21
43, 35
X=0
22
43, 33, 49
GTO 49
23
33
R↓
24
33
R↓
25
43, 33, 00
GTO 00
Binomial Distribution


26
1
1
27
44, 3
STO 3
28
43, 33, 03
GTO 03
29
33
R↓
30
45, 2
RCL 2
31
45, 0
RCL 0
32
21
Y^X
33
20
*
34
1
1
35
45, 2
RCL 2
36
30
-
37
45, 1
RCL 1
38
45, 0
RCL 0
39
30
-
40
21
Y^X
41
20
*
42
43, 33, 00
GTO 00
Negative Binomial Distribution


43
1
1
44
44, 30, 1
STO- 1
45
44, 30, 0
STO- 0
46
2
2
47
44, 3
STO 3
48
43, 33, 03
GTO 03
49
33
R↓
50
33
R↓
51
45, 2
RCL 2
52
45, 0
RCL 0
53
21
Y^X
54
20
*
55
1
1
56
45, 2
RCL 2
57
30
-
58
45, 1
RCL 1
59
45, 0
RCL 0
60
30
-
61
21
Y^X
62
20
*
63
43, 33, 00
GTO 00

Examples:

Find the number of combinations of groups of 2 out of possible 12 objects. 
12 [STO] 1, 2 [STO] 0, [ f ] [ R↓ ] (CLEAR PRGM)
Result:  66

Binomial Distribution:  Toss a coin 25 times. (trails) What is the probability of tossing 10 heads? (successes)  Assume a fair coin.  The variables n = 25, x = 10, p = 0.5 
25 [ STO ] 1, 10 [ STO ] 0, 0.5 [ STO ] 2, [ g ] [ R↓ ] (GTO) 26 [ R/S ]
Result:  0.10   (0.0974166393)

Negative Binomial Distribution:  Assume a fair coin. What is the probability that the 15th tossed of heads comes on the 25th toss of the coin?  x = 15, n = 25, p = 0.5
25 [STO] 1, 15 [STO] 0, 0.5 [ STO ] 2, [ g ] [ R↓] (GTO) 43 [ R/S ]
Result:  0.12  (0.1168999672)

This blog is property of Edward Shore, 2016.

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