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Question
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate Standard deviation of X.
Solution
We know that Standard deviation (SD) = `sqrt("Variance")`
Variance= E(X2) – [E(X)]2
E(X2) = `1 xx 2/50 + 4 xx 3/50 + 9 xx 4/50 + 16 xx 5/50 + 25 xx 10/50 + 36 xx 12/50 + 49 xx 14/50`
= `2/50 + 12/50 + 36/50 + 80/50 + 250/50 + 432/50 + 686/50`
= `1498/50`
∴ Variance (X) = `1498/50 - (26/5)^2`
= `1498/50 - 676/25`
= `(1498 - 1352)/50`
= `146/50`
= 2.92
∴ S.D = `sqrt(2.92)`
= 1.7 .....(Approx)
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