To find the probability that a random variable X, which follows a Poisson distribution with a mean (λ) of 5 , is less than 3 , we calculate P(X<3). This is equivalent to finding the sum of probabilities P(X=0),P(X=1), and P(X=2) : P(X<3)‌=P(X=0)+P(X=1)+P(X=2) ‌=‌
λ0e−λ
0!
+‌
λ1e−λ
1!
+‌
λ2e−λ
2!
Substituting λ=5, we have: P(X<3)‌=e−5(1+5+‌