91影视

The suicide rate in a certain state is $1$ suicide per $100,000$ inhabitants per month.

Since we are given that there is a rate of $1$suicide per $100,000$inhabitants, we hold that there is the rate of $4$suicides per $400,000$inhabitants. So, the number of suicides is can be expressed as a random variable $X$with allocation $X~Pois\left(4\right)$.

So,

$P(X鈮�8)=1-\underset{j=0}{\overset{7}{鈭�}}P(X=j)=1-\underset{j=0}{\overset{7}{鈭�}}\frac{4^j}{j!}{e}^{-4}鈮�0.05113$

The probability of given city found to be$0.05113$.

The suicide rate in a certain state is $1$suicide per $100,000$inhabitants per month.

Every month has the probability of $p=0.05113$that there will be more or similar to eight suicides that month. If we mark $Y$as the random variable that marks the number of months that have that property, it has approximately Poisson distribution with parameter $12路0.05113=0.61$.

Hence

$P(Y鈮�2)=1-P(Y=0)-P(Y=1)=1-e^{-0.61}-0.61e^{-0.61}鈮�0.125$

The probability of suicides found to be$0.125$.

The suicide rate in a certain state is $1$ suicide per $100,000$ inhabitants per month.

Define random variable $Z$that marks the first month in which there were $8$or more suicides. Observe that because of the nature of the problem, We have that $Z~Geom\left(p\right)$, where $p$is the probability calculated in $\left(a\right)$.

So,

$P(Z=i)=(1-p{)}^{i-1}路p$

The assumption of probability found to be$P(Z=i)=(1-p{)}^{i-1}路p$