Why Is Really Worth Probability Density Function

Like so, the normality assumption can be evaluated by superimposing a normal curve over a histogram of observed values like we saw here. 24 7. A random variable

X

{\displaystyle X}

has density

great site f

here X

{\displaystyle f_{X}}

, where

f

X

{\displaystyle f_{X}}

is a non-negative Lebesgue-integrable function, if:
Hence, if

F

X

{\displaystyle F_{X}}

is the cumulative distribution function of

X

{\displaystyle X}

, then:
Intuitively, one can think of

f

X

(
x
)

d
x

{\displaystyle f_{X}(x)\,dx}

as being the probability of

X

{\displaystyle X}

falling within the infinitesimal interval

[
x
,
x
+
d
x
]

{\displaystyle [x,x+dx]}

. .