P(X=1)=400!∗e−4≈1,83%{\displaystyle P(X=1)={\frac {4^{0}}{0!}}*e^{-4}\approx 1,83\%}
P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=∑k=034kk!∗e−4≈43,35%{\displaystyle P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=\sum _{k=0}^{3}{\frac {4^{k}}{k!}}*e^{-4}\approx 43,35\%}
P(X=4)=444!∗e−4≈19,54%{\displaystyle P(X=4)={\frac {4^{4}}{4!}}*e^{-4}\approx 19,54\%}
P(X>4)=1−P(X=4)−P(X<4)≈37,12%{\displaystyle P(X>4)=1-P(X=4)-P(X<4)\approx 37,12\%}
P(X>4|X>0)=P(X>3∩X>0)P(X>0)=P(X>3)P(X>0)=1−P(X≤3)1−P(X=0)=1−∑k=034kk!∗e−41−e−4≈57,71%{\displaystyle P(X>4|X>0)={\frac {P(X>3\cap X>0)}{P(X>0)}}={\frac {P(X>3)}{P(X>0)}}={\frac {1-P(X\leq 3)}{1-P(X=0)}}={\frac {1-\sum _{k=0}^{3}{\frac {4^{k}}{k!}}*e^{-4}}{1-e^{-4}}}\approx 57,71\%}
