Question
Find the mean, variance, and standard deviation of the random variable $x$ associated with the probability density function over the indicated interval.$$f(x)=\frac{3}{8} x^{2} ;[0,2]$$
Step 1
The expected value $E(X)$ is given by the integral of $x$ times its probability density function over the given interval. So, we have: $$E(X) = \int_{0}^{2} x \cdot \frac{3}{8} x^{2} dx$$ This simplifies to: $$E(X) = \int_{0}^{2} \frac{3}{8} x^{3} dx$$ Evaluating Show more…
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