The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. (a) What is the proba
1 answer:
Answer:
Step-by-step explanation:
From the question we are told that:
Exponential distribution mean
Distance
Generally the equation for Exponential distribution is mathematically given by
Therefore
Possion Y
Generally the equation for The probability that there are no major cracks in a 10 mile stretch of the highway is mathematically given by
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Here's another one.
See the attached picture.
See the attached picture.
First, we need to solve the differential equation.
This a separable ODE. We can rewrite it like this:
Now we integrate both sides.
We get:
When we solve for y we get our solution:
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
This a separable ODE. We can rewrite it like this:
Now we integrate both sides.
We get:
When we solve for y we get our solution:
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.