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If x is a binomial random variable, compute p(x) for each of the following cases: P(x)=n!/ (x!(n−x)!) * p^x(1−p)^(n−x)

is the formula you have to evaluate for each number set.


n=5, x=1, p = 0.2

n=4, x=2, q = 0.4

n=3, x=0, p = 0.7

n=5, x=3, p = 0.1

n=4, x= 2, q = 0.6

n=3, x=1, q = 0.9

Verified Answer :

nobillionaireNobley

P(x) = nCx p^x (1 - p)^(n - x) = n! / (x!(n - x)!) p^x q^(n - x)

For n = 5, x = 1, p = 0.2:
P(1) = 5! / (1! (5 - 1)!) 0.2^1 (1 - 0.2)^(5 - 1) = 5 0.2 0.4096 = 0.4096


For n = 4, x = 2, q = 0.4:
P(2) = 4! / (2! (4 - 2)!) (1 - 0.4)^2 0.4^(4 - 2) = 6 0.36 0.16 = 0.3456


For n = 3, x = 0, p = 0.7:
P(0) = 3! / (0! (3 - 0)!) 0.7^0 (1 - 0.7)^(3 - 0) = 1 1 0.027 = 0.027
 

For n = 5, x = 3, p = 0.1
P(3) = 5! / (3! (5 - 3)!) 0.1^3 (1 - 0.1)^(5 - 3) = 10 0.001 0.81 = 0.0081


For n = 4, x = 2, q = 0.6
P(2) = 4! / (2! (4 - 2)!) (1 - 0.6)^2 0.6^(4 - 2) = 6 0.16 0.36 = 0.3456

For n = 3, x = 1, q = 0.9
P(1) = 3! / (1! (3 - 1)!) (1 - 0.9)^1 0.9^(3 - 1) = 3 0.1 0.81 = 0.243

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