Binomial Formula: Binomial Formula n = Number of trials x = number of combination p = Probability of success in a single trial q = Probability of failure in a single trial ( i.e p+q =1) C n x a combination
Example: Example A die is tossed 3 times. What is the probability of No fives turning up 1 five
Way to solve it: Way to solve it Here, x = 0 P(x=0) = 3C0 ● (1/6^0) ● (5/6^3) = 0.5787 b) Here, x=1 P(x=1) =3C1 ● (1/6^1) ● (5/6^2) =0.3472
Mean and Standard Deviation for Binomial Distribution: Mean and Standard Deviation for Binomial Distribution The formula for mean Standard Deviation formula
Example: Example Find the mean, standard deviation and variance for the following n = 50, p = 0.85 n = 500, p = 0.9
Slide 6: μ = np σ = √ npq =50 ● (0.85) =√(50 ● 0.85 ● 0.15) =42.5 =2.52 μ = np σ = √500 ● (0.9) ● (0.1) = 500 ● (0.9) = 6.708 =450
Poisson Probability: Poisson Probability λ = number of occurrences e= 2.71828 Means it multiple by the number Example 5!=1×2×3×4×5
Example: Example Compute the probability of x for the following: λ = 9, x = 5 λ = 6, x = 3
Slide 9: (9^5 × e^-9)/5! =0.0607 b) (6^3 × e^-6)/ 3! =0.0892
Conclusion: Conclusion In the past few slide we have learn about the probability distribution of a discrete value. We also have learn about the Binomial formula and poisson formula which can be use in different situation, such as for outcome more then we use poisson , while outcome that have only for result we use binomial .