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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 a nonsymmetric probability 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. A$0$B$1$C$2$D$3$E$4$F$5\$

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