Answer:
A) [tex]P(X=x) = \binom{2}{x}.(0.908)^x.(0.092)^{2-x}[/tex]
B) Mean = 1.816
Step-by-step explanation:
We are given the following information:
We treat Stephen Curry making any given free throw as a success.
P(Stephen Curry makes any given free throw) = 0.908
Since the probability for the free throw is equal for each trial and free throws are independent.
Then the number of free shots follows a binomial distribution.
A) Probability distribution
[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.
Here n = 2, p = 0.908
[tex]P(X=x) = \binom{2}{x}.(0.908)^x.(1-0.908)^{2-x}\\\\P(X=x) = \binom{2}{x}.(0.908)^x.(0.092)^{2-x}[/tex]
Now x can take values 0, 1 , 2
Putting values, we get,
[tex]P(x = 0) = 0.008464\\P(x = 1) = 0.167072\\P(x = 2) = 0.82446[/tex]
B) Mean of X
[tex]\mu = np = 2(0.908) =1.816[/tex]
Thus, the mean number of free shots made by Stephen Curry is 1.816
