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X is a binomial variable with n = 20. What is the mean of X if it is known that x is symmetric?
- a)5.
- b)10 .
- c)2.
- d)8.
Correct answer is option 'B'. Can you explain this answer?
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X is a binomial variable with n = 20. What is the mean of X if it is k...
Mean of a Symmetric Binomial Distribution
- A binomial distribution is symmetric if p = 0.5 or if n is odd.
- If X is a symmetric binomial variable with n trials, then the mean is simply the midpoint of the distribution.
- The midpoint is calculated as (n+1)/2.
Calculation for the Given Problem
- The problem states that X is a binomial variable with n = 20 and is symmetric.
- Therefore, the midpoint of the distribution is (20+1)/2 = 10.5.
- However, since X can only take on integer values, the mean is rounded down to the nearest integer, which is 10.
- Therefore, the correct answer is option 'B' - 10.
- A binomial distribution is symmetric if p = 0.5 or if n is odd.
- If X is a symmetric binomial variable with n trials, then the mean is simply the midpoint of the distribution.
- The midpoint is calculated as (n+1)/2.
Calculation for the Given Problem
- The problem states that X is a binomial variable with n = 20 and is symmetric.
- Therefore, the midpoint of the distribution is (20+1)/2 = 10.5.
- However, since X can only take on integer values, the mean is rounded down to the nearest integer, which is 10.
- Therefore, the correct answer is option 'B' - 10.
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X is a binomial variable with n = 20. What is the mean of X if it is k...
N x p =20 x 0.5 =10
(in symmetry of binomial distribution value of p is always equal to 0.5)
(in symmetry of binomial distribution value of p is always equal to 0.5)
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X is a binomial variable with n = 20. What is the mean of X if it is known that x is symmetric?a)5.b)10 .c)2.d)8.Correct answer is option 'B'. Can you explain this answer?
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