I must calculate the probability : $P(43 < X < 63)$
How do we even calculate the probability between two numbers ? I have a formula for the situation when : $P(X > a)= e^{‐λa}$. Must I use the density function in this situation ?
By the way, $λ =\dfrac{1}{25}$.
My guess is that I'll have to do some substraction of areas but I'm not sure ....
$\endgroup$1 Answer
$\begingroup$If the cdf is $F_X(x)$, then $$\Pr(X\le b)=F_X(b)$$ and $$\Pr(a<X\le b)=F_X(b)-F_X(a)$$
The exponential cdf is $F_X(x)=1 − e^{-\lambda x}$. You can substitute the $\le$ with $<$, since the cdf is continuous.
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