Question 29.9: A random variable has p.d.f. given by f (x) = 1 / 2√x 1 ≤ x ......
A random variable has p.d.f. given by
f(x)={\frac{1}{2{\sqrt{x}}}} 1 ≤ x ≤ 4
Calculate the expected value of x.
Step-by-Step
\mu=\int_{1}^{4}x\frac{1}{2\sqrt{x}}\,\mathrm{d}x=\int_{1}^{4}\frac{\sqrt{x}}{2}\,\mathrm{d}x \\
=\left[\frac{x^{3/2}}{3}\right]_{1}^{4}=\frac{7}{3}
So, if several values of x are measured, the mean of these values will be near to {\frac{7}{3}}. As more and more values are measured the mean will get nearer and nearer to {\frac{7}{3}}.
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