Answer:
y = -(3/7)x + 2
Step-by-step explanation:
(see attached)
recall that the slope-intercept form of a linear equation is
y = mx + b
where m = slope = given as -(3/7)
and b = y-intercept = 2
substituting these values into the eqation:
y = mx + b
y = -(3/7)x + 2
I hope I helped you^_^
Answer:
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: