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I know that to know the Distribution function I got to integrate the Density function from "-oo" to "x", but how to do the inverse?

user2993157
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Differentiate.${}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}$

André Nicolas
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  • can you even tell me why I got to integrate from -oo to x in the first case? – user2993157 Nov 16 '13 at 01:11
  • The integral gives you the area under the density curve, from $-\infty$ to $x$. Another way of thinking about pprobability densities is that you have a "wire" of variable density, of total mass $1$. You are trying to find the mass of the wire from $-\infty$ to $x$. So you divide the wire into very small bits of length "$dt$". The weight of the piece of length $dt$, from $t$ to $t+dt$, is about $f(t),dt$. To find the total mass, you "add up" (in reality, integrate). – André Nicolas Nov 16 '13 at 01:18