a)"P(X=0)=\\frac{2^0}{0!}e^{-2}=\\frac{1}{1}e^{-2}=e^{-2}"
"P(X=1)=\\frac{2^1}{1!}e^{-2}=\\frac{2}{1}e^{-2}=2e^{-2}"
"P(X=2)=\\frac{2^2}{2!}e^{-2}=\\frac{4}{2}e^{-2}=2e^{-2}"
"P(X=3)=\\frac{2^3}{3!}e^{-2}=\\frac{8}{6}e^{-2}=\\frac{4}{3}e^{-2}"
"P(X=4)=\\frac{2^4}{4!}e^{-2}=\\frac{16}{24}e^{-2}=\\frac{2}{3}e^{-2}"
"P(X=5)=\\frac{2^5}{5!}e^{-2}=\\frac{32}{120}e^{-2}=\\frac{4}{15}e^{-2}"
"P(X=6)=\\frac{2^6}{6!}e^{-2}=\\frac{64}{720}e^{-2}=\\frac{4}{45}e^{-2}"
b)"P(X\\le 0)=P(X=0)=e^{-2}"
"P(X\\le 1)=P(X=0)+P(X=1)=3e^{-2}"
"P(X\\le 2)=P(X=0)+P(X=1)+P(X=2)=5e^{-2}"
"P(X\\le 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=\\frac{19}{3}e^{-2}"
"P(X\\le 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=7e^{-2}"
"P(X\\le 5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=\\frac{109}{15}e^{-2}"
"P(X\\le 6)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)=\\frac{331}{45}e^{-2}"
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