Question

Calculate the probability of an exponential distribution rate of cars?

Answer 1

The probability of an exponential distribution rate of cars can be calculated using the formula
`P(x < t) = 1 - e^(^-^r^t^)`, where P(x < t) is the probability that the time until the next car passes is less than t, r is the rate of cars passing (in cars per minute), and e is the base of the natural logarithm.

Step-by-step explanation:

The probability of an exponential distribution rate of cars can be calculated using the formula:

`P(x < t) = 1 - e^(^-^r^t^)`

Where P(x < t) is the probability that the time until the next car passes is less than t, r is the rate of cars passing (in cars per minute), and e is the base of the natural logarithm.

For example, if the rate of cars passing is 5 cars per minute, and we want to calculate the probability that the next car will pass within the next 20 seconds:

`P(x < 20 seconds) = 1 - e^(^-^5^ x ^(^2^0^/^6^0^))`

=
`1 - e^(^-^5^/^3^)`

≈ 0.9502