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Statement 1: If a random variable X has a binomial distribution with mean a and variance b, then a²/(a-b) is a positive integer.
Statement 2: For a binomial distribution, the mean is greater than the variance.
Choose the correct option:
(a) Statement 1 is false and Statement 2 is true
(b) Statement 1 is true and Statement 2 is true, and Statement 2 correctly explains Statement 1
(c) Statement 1 is true and Statement 2 is true, but Statement 2 does not correctly explain Statement 1
(d) Statement 1 is false and Statement 2 is false
- (a)
- (b)
- (c)
- (d)
Correct answer: (c)
Solution
Statement 1 is true because for a binomial distribution, the mean (a) and variance (b) can be expressed in terms of the number of trials and probability, leading to the conclusion that a²/(a-b) is a positive integer. Statement 2 is also true as, in a binomial distribution, the mean is indeed greater than the variance when the probability of success is less than 0.5, but it does not explain why the first statement holds.
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