Y Dosraniad Poisson The Poisson Distribution Maer Dosraniad

Y Dosraniad Poisson The Poisson Distribution Mae’r Dosraniad Poisson yn cael ei ddefnyddio pan mae gennym nifer cyfartalog y troeon mae digwyddiad yn digwydd. The Poisson Distribution is used when we have the average number of times an event occurs. e. e. nifer y galwadau ffôn a dderbynnir mewn swyddfa mewn 1 diwrnod, the number of phone calls received in an office in 1 day, nifer y diffygion mewn hyd penodol o ddefnydd, the number of flaws along a specified length of material, nifer cymedrig y damweiniau a geir ar ddarn penodol o’r A 470 mewn mis. the mean number of accidents along a specific stretch of the A 470 in a month.

Os oes gan X ddosraniad Poisson, rydym yn ysgrifennu If X has a Poisson distribution, we write X ~ Po ( μ ) μ = y cymedr μ = the mean P(X = x) = e-µ µ x x! Mae’n bosibl hefyd defnyddio tablau i ddarganfod tebygolrwydd ar gyfer dosraniad Poisson. It is also possible to use tables to find the probability for the Poisson distribution.

Cymedr ac Amrywiant y Dosraniad Poisson The Mean and Variance of the Poisson Distribution Mae’r cymedr yn cael ei roi i ni fel µ mewn dosraniad Poisson, ac mae’r amrywiant yn hafal i’r cymedr bob amser. The mean is given to us as µ and the variance is always equal to the mean in a Poisson distribution. E(X) = Var(X) = µ Cofiwch mai ail-isradd yr amrywiant yw’r gwyriad safonol. Remember that the standard deviation is the square root of the variance. Gwyriad Safonol = √Var(X) = √µ Standard Deviation = √Var(X) = √µ

Enghraifft - Example Mae gan X ddosraniad Poisson, cymedr 5. Darganfyddwch X has the Poisson distribution with mean 5. Find a) P(X = 4) b) P(X ≥ 6) c) P(2 ≤ X ≤ 4) d) P(X < 2) e) gymedr ac amrywiant Y pan mae Y = 4 X - 2

X ~ Po ( 5 ) a) P(X = 4) = e-µ µ x = e-5 54 = 0. 175 x! 4! b) P(X ≥ 6) = 0. 384 ( yn defnyddio’r tablau) (using tables) c) P(2 ≤ X ≤ 4) = P(X ≥ 2) - P(X ≥ 5) = 0. 9596 – 0. 5595 = 0. 4001 d) P(X < 2) = P(X = 0) + P(X = 1) = e-5 50 + e-5 51 0! 1! = 0. 00674 + 0. 0337 = 0. 0404 e) E(Y) = E(4 X – 2) = 4 E(X) - 2 = 4 x 5 - 2 = 18 Var(Y) = Var(4 X – 2) = 42 Var(X) =16 x 5 = 80

Ymarfer/Exercise 4. 6 a 4. 6 b 4. 6 c Mathemateg - Ystadegaeth Uned S 1 – CBAC Mathematics Statistics Unit S 1 - WJEC