How many of the following situations are possible? The student is encouraged to come up with graphical example(s) in cases where the situation is possible.

i.A random variable $X$ with mean=$0$, has anonsymmetricprobability density function $f(x)$ which is positive in the interval [-5,5] and zero everywhere else.

ii.A probability density function $f(x)$ is nonzero for all real numbers $x$.

iii.A probability density function $f(x)$ is nonzero in interval $[a,b]$ where $a$ and $b$ are real numbers such that $a

iv.A probability density function $f(x)$ is nonzero for all real numbers $x$ except at $x=0$, monotonically increasing in the interval $(-\infty,0)$ and monotonically decreasing in the interval $(0,\infty)$.

v.A random variable $X$ has probability density function $f(x)$ such that $f(0)=10$ if the outcome of $X$ is zero and $f(0)=5$ if the outcome of $X$ is not zero.

Select an assignment template