Can a polygon be a pentagon yes or no answer!


Yes, a pentagon can be a polygon.

Any shape with straight sides can be a polygon, including hexagons, pentagons, triangles, squares, rectangles, etc. But this does not include shapes such as a circle or oval since they do not have straight sides.

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 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:

The cumulative distribution for this function is given by:

We know the value for the mean on this case we have that :

Solution to the problem

Part 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?

Part b

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

The variance for the esponential distribution is given by:

And the deviation would be:

And the mean is given by

Two deviations correspond to 5.540, so we want this probability:

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

For this case we want this probablity: