A continuous random variable has pdf $f (x) = \frac{x ^{2}}{9}$ for $0 \leq x \leq 3$ and $0$ elsewhere. The median $m$ satisfies:

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Evaluate the indefinite integral $\int \frac{2 x}{x ^{2} + 5} d x$ .
Calculate the area enclosed by the curve $y = x^{2}$ and the line $y = 4$ .
Evaluate $\int_{0}^{π /4} sec^{2} (x) d x$ .
A continuous random variable $X$ has probability density function $f (x) = k x$ for $0 \leq x \leq 4$ , and $f (x) = 0$ elsewhere. What is the val…
For the random variable $X$ with PDF $f (x) = \frac{1}{8} x$ on $[0, 4]$ , calculate the expected value $E (X)$ .
Scores on a statewide exam are normally distributed with mean $μ = 70$ and standard deviation $σ = 8$ . What is the z-score of a stude…