Question

Let t represent the distance between major cracks in a highway. t follows an exponential distribution with a mean of 5 miles. what is the variance of t? (do not include units in your answer) A.25 B.5 C.12.5 D.6.25

Answer 1

First, let's understand the behaviour of an exponential distribution.

The exponential distribution, which is widely used for modelling time intervals in a Poisson point process, is also characterized by having the mean equal to the reciprocal of its parameter lambda (λ).

The variance of an exponential distribution, on the other hand, is given by the square of the mean of the distribution. This means that if the mean of the distribution is a certain value, the variance will be the square of that value.

Now, coming to our problem, we are given that t follows an exponential distribution and its mean (average distance between major cracks) is 5 miles.

Since variance for an exponential distribution equals the square of the mean, let's calculate the variance.

We'll substitute the mean value into our variance formula,

variance = (mean)^2

Substitute the given mean value (5) into the formula,

variance = (5)^2
variance = 25

Therefore, the variance of t is 25 which corresponds to option A.