(12C) Combination/Binomial Distribution/Negative Binomial Distribution
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08-31-2016, 07:47 PM
Post: #1
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(12C) Combination/Binomial Distribution/Negative Binomial Distribution
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. Code:
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) |
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