Question

How would I do a question like this:

Create the probability distribution table (correct to 4 decimal places) for a binomial distribution with n=3 and p=0.4. I also have to show the full calculation for each row.

Answer 1

Solution:

X follows the Binomial(n = 3 , p = 0.4)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Here , n = 3

So , possible values if x are 0,1,2,3

P(X = 0) = (₃C ₀) * 0.4⁰ * (1 - 0.4)^{3 - 0} = (₃C ₀) * 0.4⁰ * (0.6)³ = 0.216

P(X = 1) = (₃C ₁) * 0.4¹ * (1 - 0.4)^{3 -1} = (₃C ₁) * 0.4¹* (0.6)² = ​​​​​​​0.432

P(X = 2) = (₃C ₂) * 0.4²* (1 - 0.4)^{3 - 2}  = (₃C ₂) * 0.4²* (0.6)¹ = ​​​​​​​0.288

P(X = 3) = (₃C ₃) * 0.4³ * (1 - 0.4)^{3 - 3} = (₃C ₃) * 0.4³ * (0.6)⁰ = ​​​​​​​0.064

x	0	1	2	3
P(X = x)	0.216	0.432	0.288	0.064