(a) If $f(x)=\left\{\begin{array}{cc}0 & x<2 \\ \frac{1}{18}(2 x+3) & 2 \leq x<4 \\ 0 & x>4\end{array}\right.$ is the probability density function of a random variable. Find Mean and distribution function.

Explanation

The probability density function is given by $f(x)=\left\{\begin{array}{cc}0 & x<2 \\ \frac{1}{18}(2 x+3) & 2 \leq x<4 \\ 0 & x>4\end{array}\right.$. Mean is calculated by integrating the product of $x$ and the probability density function over the given interval. Distribution function is calculated by integrating the probability density function over the given interval.

(a) If $f(x)=\left\{\begin{array}{cc}0 & x<2 \\ \frac{1}{18}(2 x+3) & 2 \leq x<4 \\ 0 & x>4\end{array}\right.$ is the probability density function of a random variable. Find Mean and distribution function.

Explanation

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