The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
Question
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are
Solution
The first three moments of a distribution about a point (in this case, 2) are given as 1, 16, -40. These are the first, second, and third central moments about 2, respectively.
The first moment about 2 is the mean (μ) of the distribution. So, μ = 1.
The second moment about 2 is the variance (σ^2) of the distribution plus the square of the mean (μ^2). So, 16 = σ^2 + (1)^2. Solving for σ^2, we get σ^2 = 16 - 1 = 15.
Therefore, the mean of the distribution is 1 and the variance is 15.
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