2. A taxi company has three cabs. Calls come in to the dispatcher at times of a Poisson process with rate 2 per hour. Suppose that each requires an exponential amount of time with mean 20 minutes, and that callers will hang up if they hear there are no cabs available. (a) What is the probability all three cabs are busy when a call comes in

0.406

Step-by-step explanation:

Let us make the number of cabs available to be x.

Number of calls is distributed as Poisson(\lambda =2) and

the availability of cab is distributed as Exponential(\theta =3).

Therefore, the probability all three cabs are busy when a call comes in is given by;

P(X=0)=\frac{e^{-\lambda}\lambda^x}{x!}\theta e^{-\theta x}=\frac{e^{-2}2^0}{0!}3e^{-3\times 0}= 0.406

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it