Question

Suppose the response time X at a certain on-line computer terminal (the elapsed time between the end of a user's inquiry and the beginning of the system's response to that inquiry) has an exponential distribution with expected response time equal to 5 seconds.

a) Find E(X)

b) What is lamda?

c) Find P(5<=X<=10)

d) Find the 60th %tile.

Answer 1

a)

We are given that X is the response time at a certain on-line computer terminal. Moreover, we are given that the expected response time is equal to 5 seconds. Thus, we get:

E(X) = 5 seconds [ANSWER]

b)

We are given that the distribution of X is exponential, say the rate parameter for the distribution of X is λ.

Thus, E(X) = 1/λ

But in part a), we found that E(X) = 5, thus we get:

1/λ = 5

=> λ = 1/5 [ANSWER]

c)

In part b), we found that the distribution of X is exponential with rate parameter λ = 1/5. Thus, the cumulative distribution function of X is given by:

Now, the required probability is given by:

d)

Let 'a' denote the 60th percentile, then a satisfies:

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