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Given the probability density functio (p.d.f) of a continuos random variable X as. `f(x)=(x^(2))/(3),-1 lt x lt2` Determine the cumulative distribution function (c.d.f) X and hence find `P(X lt1),P(X gt0), P(1 lt X lt 2)`. |
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Answer» c.d.f. of the continuous variable is given by `f(x) = underset(-1)overset(x) int y^(2)/3 dx ` ` = [y^(3)/9]_(-1)^(x)` ` = (((x^(3)+1))/9) , x in R` Consider ` P (x lt 1) = f(1) = ((1)^(3) + 1)/9 = 2/9` ` P(x le -2) = 0` ` P(x gt 0) = 1 - P (x le 0) ` ` = 1 - f(0) = 1 - (1/9) = 8/9` ` P(1 lt x lt 2) = f(2) - f (1) = 1 - 2/9 = 7/9` |
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