David is deciding to buy either a new car or a used car that has been driven 10,000 miles. For each car, find the probability that he can drive it for an extra 20,000 miles in the following scenarios.

(a) The total mileage that both cars can be driven before they completely break down is an exponential random variable with mean 20 thousands miles.
(b) The total mileage that both cars can be driven before they completely break down is uniformly distributed over (0, 40,000).

a)

b)

Step-by-step explanation:

a) In the given case,

Mileage of the cars =

The PDF is

The CDF is

For new car the probability will be

For the used car probability is

b) For the case given in this part the mileage of the cars is Uniform (0,40000)

The PDF is

The CDF is

For the new car probability is

For the old car probability is,

step-by-step explanation:

once you graph it hit 2nd (the blue button) and graph

that takes you to a table of coordinates

on the left is x coordinates and on the right is y coordinates and an empty box

(you may have to scroll up/down in order to get ( x, 0)

1 3 5

step-by-step explanation:

i took the test: )