What is the mean and variance of a random variable with the following probability density function?: $f(x) = 3x^2 if -1 < x < 1$ ; 0 otherwise

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Answer 1 · 2015-11-03T04:51:49

Mean $E (X) = 0$ and variance $"Var" (X) = 6/5$ .

Note that

$E (X) = int_-1^1 x * (3x^2 ) " " dx$
$= int_-1^1 3x^3 " " dx$
$= 3 * [ x^4 /4 ]_( "(" - 1, 1 ")" )$
$=0$

Also note that

$"Var" (x) = E (X^2)- (E(X))^2$
$= 3 * [ x^5/5 ] _("("- 1, 1")") - 0^2$
$= 3/5 * (1 + 1)$
$= 6/5$

What is the mean and variance of a random variable with the following probability density function?: f(x) = 3x^2 if -1 < x < 1f(x) = 3x^2 if -1 < x < 1; 0 otherwise