Question

Let Y be the number of times Paul gets the flu during one 12-month period. Y is Poisson with λ = 1.45.

(a) List the possible values of Y.

(b) What is the probability that Paul gets the flue at least once during the next 12-month period?

Answer 1

Let Y be the number of times Paul gets the flu during one 12-month period. Y is Poisson with $\small \lambda$ = 1.45.

If Y is Poisson with $\small \lambda$ then the probability mass function of Y

$\small P(Y=y)=\frac{e^{-\lambda }\lambda ^{y}}{y!}\; \; \; \; \; y=0,1,2,3,4,.........$

Y is Poisson with λ = 1.45

$\small P(Y=y)=\frac{e^{-1.45}\times 1.45 ^{y}}{y!}\; \; \; \; \; y=0,1,2,3,4,.........$

(a) List the possible value of Y : 0,1,2,3,4,5,......................

b) Probability that Paul gets the flu at least once during the next 12-month period = P(Y$\small \geq$1) = 1 - P(Y=0)

Substituting , y=0 in the above pmf ( e is approximately equal to 2.71828)

$\small P(Y=0)=\frac{e^{-1.45}\times 1.45 ^{0}}{0!}=e^{-1.45}= 2.71828^{-1.45}=0.2346$

P(Y$\small \geq$1) = 1 - P(Y=0) = 1-0.2346 = 0.7654

Probability that Paul gets the flu at least once during the next 12-month period = 0.7654