I have a series of six probability density functions $X$, each of which satisfies at least one of the following conditions:
- $X$ is non-negative.
- $X$ can take any positive value.
- $X$ is a reasonably realistic pdf for a model of a share price of a bank in a year's time.
- The probability of $X$ taking a value in the range $(a, b)$ is the same as the chance of $X$ taking a value in the range $(-b, -a)$.
- $X$ is a reasonably realistic pdf for a model of human life expectancy.
- There is a number $a$ such that $P(x> a) \geq 2 P(x> 2a)$.
Which of the following six curves (ignoring scale) would be the potential candidates for these mathematical descriptions? Are multiple matches possible? What axes and scales would you choose in each case?