Question

In: Statistics and Probability

Let X denote the distance (in meters) that an animal moves from its birth site to...

Let X denote the distance (in meters) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter θ = 72.46. Find the probability that the distance is:

a) at most 100 meters b) at most 200 meters

c) between 100 and 200 meters

Solutions

Expert Solution

Let X denote the distance (in meters) that an animal moves from its birth site to the first territorial vacancy it encounters.

Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter θ = 72.46

i.e. x~exp (θ = 72.46)

The probability density function of x is:

The distribution function of x is is:

a)The probability that the distance is at most 100 meters

The probability that the distance is at most 100 meters 0.7484

b)The probability that the distance is at most 200 meters.

The probability that the distance is at most 200 meters 0.9367

c) The probability that the distance is between 100 and 200 meters.

The probability that the distance is between 100 and 200 meters is 0.1882

orchestra answered 1 year ago

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