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The maximum value of the variance of a binomial distribution with parameters n and p is
- a)n/2
- b)n/4
- c)np (1 – p)
- d)2n
Correct answer is option 'B'. Can you explain this answer?
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The maximum value of the variance of a binomial distribution with para...
The maximum value of the variance of a binomial distribution with parameters n and p is np(1-p).
To find the maximum value of the variance, we can take the derivative of the variance formula with respect to p and set it equal to zero.
Variance = np(1-p)
dV/dp = n(1-p) - np
Setting this equal to zero and solving for p, we get:
n(1-p) - np = 0
n - np - np = 0
n - 2np = 0
n = 2np
1 = 2p
p = 1/2
Substituting this value of p back into the variance formula, we get:
Variance = n(1/2)(1-1/2)
Variance = n/2
Therefore, the maximum value of the variance is n/2.
So the correct answer is a) n/2.
To find the maximum value of the variance, we can take the derivative of the variance formula with respect to p and set it equal to zero.
Variance = np(1-p)
dV/dp = n(1-p) - np
Setting this equal to zero and solving for p, we get:
n(1-p) - np = 0
n - np - np = 0
n - 2np = 0
n = 2np
1 = 2p
p = 1/2
Substituting this value of p back into the variance formula, we get:
Variance = n(1/2)(1-1/2)
Variance = n/2
Therefore, the maximum value of the variance is n/2.
So the correct answer is a) n/2.
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The maximum value of the variance of a binomial distribution with parameters n and p isa)n/2b)n/4c)np (1 – p)d)2nCorrect answer is option 'B'. Can you explain this answer?
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