A statistical probability distribution P(t) is to be constructed from the following nine data points, where t is the time: P(1) = 0, P(2) = 1.0, P(3) = 2.5, P(4) = 4.0, P(5) = 5.0, P(6) = 4.0, P(7) = 2.5, P(8) = 1.0, and P(9) = 0. Is this probability distribution symmetrical or asymmetrical? What

Question

A statistical probability distribution P(t) is to be constructed from the following nine data points, where t is the time: P(1) = 0, P(2) = 1.0, P(3) = 2.5, P(4) = 4.0, P(5) = 5.0, P(6) = 4.0, P(7) = 2.5, P(8) = 1.0, and P(9) = 0. Is this probability distribution symmetrical or asymmetrical? What is the average value or the mean value of the data points? What is the variance of the distribution and what is its standard deviation?

Accepted Answer

The distribution is definitely symmetrical. The mean of the data points is [latex]⟨v⟩ = Σ_nv_n/N = 2.222[/latex]. The variance V is equal to the average of the squares less the square of the average or V = ⟨v²⟩ − ⟨v⟩² = 7.944 − 4.937 = 3.007. The standard deviation is the square root of the variance, so [latex]σ = \sqrt{V} = 1.732[/latex].

Question 23.4: A statistical probability distribution P(t) is to be constru......

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