What does this probability equation mean? I'm learning this in high school and I'm not particularly understanding the Math symbols/notations yet. What does this mean? What is Normal and how does c | 2500,50 work when calculating?
() = 0.3⋅(|2500,50) + 0.4⋅(|3000,100) + 0.3⋅(|3250,80)          (.1)
and
()=(|8,25)         (.2)
 A: $p(c)$ means the density at $c$, for the first one you have a unimodal distribution comprised of three normal densities with two lesser modes. The normal distribution is an important distribution in statistics that is used to model many physical phenomena and looks like a bell curve. $\text{Normal}(c|\mu, \sigma^2)$ refers to the normal density with parameters mean and standard deviation $\mu, \sigma$ and $\text{Gamma}(s|\alpha, \beta)$ refers to the gamma density with parameters shape and rate. The gamma density looks like $1/x$ for $\alpha < 1$, $e^{-x}$ for $\alpha=1$, and a hump starting a $(x,y)=(0,0)$ for $\alpha > 1$ and has support $s\ge0$ (the possible values of $s$). The first one has form $\frac{1}{\sigma\sqrt{2\pi}}\exp{-\frac 1 2\left(\frac{c-\mu}{\sigma}\right)^2}$ and the second one is $\frac{\beta^\alpha}{\Gamma(\alpha)}s^{\alpha-1}e^{-\beta s}$. The density tells you how likely you are to observe a value of $c$ or $s$ inside an interval and the area under it integrates to $1$, also it can never be negative.
