Let x denote the distance (m) 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 λ = 0.01352. (a) what is the probability that the distance is at most 100 m? at most 200 m? between 100 and 200 m? (round your answers to four decimal places.)

Answer with Step-by-step explanation:

We are given that

X=Distance (m) that animal moves from its birth site to the first territorial vacancy it encounters.

Parameter=

Exponential distribution of probability is given by

Cumulative distribution is given by

Where

a.We have to find the probability that the distance is at most 100m.

Hence, the probability that the distance is at most 100 m=0.7413

b.

Hence, the probability that the distance is at most 200m =0.9331

c.

Hence, the probability that the distance between 100 m and 200 m=0.1918

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: