Question
Find the expected value and variance for each random variable whose probability density function is given. When computing the variance, use formula (5).$$f(x)=12 x(1-x)^{2}, 0 \leq x \leq 1$$
Step 1
The expected value E(X) is given by the integral of x times the probability density function f(x) over the interval [0,1]. So we have: \[E(X) = \int_{0}^{1} x f(x) dx = \int_{0}^{1} x \cdot 12x(1-x)^{2} dx\] This simplifies to: \[E(X) = \int_{0}^{1} Show more…
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