For binomial distribution E(x) = 2, V(x) = 4/3. Find the value of n.(a) 3(b) 4(c) 5(d) 6
Question
Solution
In a binomial distribution, the expected value E(x) is equal to np and the variance V(x) is equal to npq, where n is the number of trials, p is the probability of success, and q is the probability of failure (1-p).
Given E(x) = 2 and V(x) = 4/3, we can set up the following equations:
np = 2 npq = 4/3
We can solve the first equation for p:
p = 2/n
Substitute p into the second equation:
n(2/n)q = 4/3 2q = 4/3 q = 2/3
Substitute q back into the first equation:
n(2/n)(2/3) = 2 2(2/3) = 2 n = 3
So, the value of n is 3, which corresponds to option (a).
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