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) = (_{3}C _{0}) * 0.4^{0} * (1 -
0.4)^{3 - 0} = (_{3}C _{0}) *
0.4^{0} * (0.6)^{3} = 0.216

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

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

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

x | 0 | 1 | 2 | 3 |

P(X = x) | 0.216 | 0.432 | 0.288 | 0.064 |

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