The random variable X follows a Poisson distribution with standard deviation 2. Find P(X ≤ 3).

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In a Poisson distribution, variance=mean, and SD^2=variance, so mean=4. P(X)=e^-m*m^X/X!. P(X<3)=P(0)+P(1)+P(2)+P(3)=e^-4(1+4+16/2+64/6)=71(e^-4)/3=0.4335.

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