The mean of a continuous random variable is the balance, Basic Statistics

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The mean of a continuous random variable is the balance

Find the mean of the sum. Given Figure displays the density curve of the sum Y = X₁ + X₂ of two independent random numbers, each uniformly distributed between 0 and 1.

(a) The mean of a continuous random variable is the balance point of its density curve. Use this fact to find the mean of Y from Figure.

(b) Use the same fact to find the means of X₁and X₂. (They have the density curve pictured in given Figure. Verify that the mean of Y is the sum of the mean of X₁ and the mean of X₂.

Figure

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