91影视

By the Journal of Economic Psychology (September 2008),

The rain frequencies of July and August follow a Poisson distribution with a mean of 10

The estimated probability of occurrence of two events fire and theft is 0.0001

a.

x is a Poisson distribution with a mean of 10,

Here, rain on exactly 24 days in July, i.e., $X=24\mathrm{and}位=10$

$$\begin{gathered} P\left(x=24\right)=\frac{e^{-位}{位}^x}{x!} \\ =\frac{e^{-10}{10}^{24}}{24!} \\ =0.00007317 \\ P\left(x=24\right)=0.00007317 \end{gathered}$$

Therefore, the probability of rain for exactly 24 days in July is, 0.00007317

b.

x is a Poisson distribution with a mean of 10,

Here, rain on exactly 23 days in August, i.e.,$\mathrm{x}=23\mathrm{and}\mathrm{位}=10$

$$\begin{gathered} P\left(x=24\right)=\frac{e^{-位}{位}^x}{x!} \\ =\frac{e^{-10}{10}^{24}}{23!} \\ =0.00017561 \\ P\left(x=23\right)=0.00017561 \end{gathered}$$

Therefore, the probability of rain for exactly 23 days in August is, 0.000175661

c.

In the case, of part (a),

The approximate probability of rain for exactly 24 days in July is, 0.00007317, i.e., 0.0001

And, in the case of part (b),

The probability of rain for exactly 23 days in August is 0.000175661, i.e., 0.0002

So, probability in part(a) is very close to the exact probability given in the question, but in part(b) the probability differs more from the exact probability given in the question.

So, part(a) is a good approximation and is better than part(b)