Respuesta :
Answer:
Probability Mass Function:
x: 0 1 2 3
P(x): 0.000064 0.004608 0.115902 0.884736
Step-by-step explanation:
We are given the following information:
We treat correct classification as a success.
P(correct classification) = 0.96
Then the number of classification follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 3 and x = 0, 1, 2, 3
We have to evaluate:
[tex]P(x = 0)\\= \binom{3}{0}(0.96)^0(1-0.96)^3\\=0.000064[/tex]
[tex]P(x = 1)\\= \binom{3}{1}(0.96)^1(1-0.96)^2\\=0.004608[/tex]
[tex]P(x = 2)\\= \binom{3}{2}(0.96)^2(1-0.96)^1\\=0.115902[/tex]
[tex]P(x = 3)\\= \binom{3}{3}(0.96)^3(1-0.96)^0\\=0.884736[/tex]
PMF:
x: 0 1 2 3
P(x): 0.000064 0.004608 0.115902 0.884736
