Mathematics: Please help this teacher didn’t explain a piece of flaky salt to me

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? We want this probability At most 3 hours?b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? What is the probability that it is less than the mean value by more than one standard deviation?Step-by-step explanation:Previous conceptsThe exponential distribution is the probability distribution of the time between events in a Poisson...

Please help this teacher didn’t explain a piece

Ответ:

Reward18

07.01.2021

Mathematics

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X 2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

P(X 2.725 + 2*5.540) = P(X13.62) = 1-P(X

What is the probability that it is less than the mean value by more than one standard deviation?

P(X

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$