Mean Questions

The probability density function for a continuous random variable $x$ is:$f(x)=\{\begin{array}{ll}\frac{x}{6},& 0\le x<2\\ \frac{1}{3},& 2\le x<4\\ -\frac{x}{6}+1,& 4\le x<6\end{array}$ The mean value of $x$ is:

A fair die is tossed thrice. If the probabilities of zero, one, two, and three successes are $8/27,4/9,2/9,\text{ and }1/27$ respectively, find the mean of the number of successes.

The mean of the probability distribution function given by the following table will be:\begin{center}\begin{tabular}{|c|c|c|c|c|c|}\hline$x$ & 1 & 2 & 3 & 4 & 5 \ \hline$P(x)$ & 0.2 & 0.35 & 0.25 & 0.15 & 0.05 \ \hline\end{tabular}\end{center}

The mean of the numbers obtained on throwing a die having written $5$ on four faces, $4$ on three faces, $3$ on two faces and $2$ on one face is?