Moderate# Determining Mean and Variance of a Discrete Random Variable

STATS-ZA1IEJ

Suppose $X$ is a random variable whose probability mass function $p(x)$ is given by:

$$ p(x)=\begin{cases} .1 &\mbox{if } x=.15, .25\\\ .25 &\mbox{if } x=.05, .2\\\ .3 &\mbox{if } x=.35 \end{cases} $$

How many of the following statements are **TRUE**?

i.The mean of $X$ is $.2075$ and variance of $X$ is $.0128$ (after some rounding).

ii.The mean of $X$ can be obtained from the formula $\displaystyle\sum_{x} xp(x)$ where $x$ is an outcome of $X$.

iii.The standard deviation of $X$ can be obtained from the formula $\displaystyle\sum_x (x-.2075)^2p(x)$ where $x$ is an outcome of $X$.

iv.The variance of $X$ can be approximated by computing the variance of a dataset created by carrying out experiment $X$ many times.

v.If $Y=X+1$, then mean of $Y$ is $1.2075$.