A ping test determines whether a client (computer, smartphone, or similar device) communicates with another device across a network.

coexpennan

coexpennan

Answered question

2021-09-12

A ping test determines whether a client (computer, smartphone, or similar device) communicates with another device across a network. Assume that the probability of response to a test is 3/4. The test involves a large number of runs and it continues until the first response is recorded. Define the random variable X as the number of runs of the test required to terminate the experiment. Suppose that the condition of one run does not affect that of another.
a. Determine the probability distribution of X.
b. Let A be defined as the event that the experiment ends after an even number of repetitions. Evaluate P(A).

Answer & Explanation

delilnaT

delilnaT

Skilled2021-09-13Added 94 answers

a) Probability of resposnse to a test = 3/4
Let x be a random variable which denotes the number sums of the test required to terminate the experiment.
The experiment terminates with the recording of the first response. Hence, with the second rerording of first success.
So,Hence, X follows a geometric distribution i.e. The probability that the first occurence of success requires k independent trials, each with probability P1 then,
P[x=k]=(1p)k1p, k=1,2,3...
b) The experiment ends after an even number of repetitions.
P[A]=P[x=2]+P[x=7]+P[x=6]+

=qp+q3p+q5p+
=qp[1+q2+q7+]
qp[11q2][sum of infinite geometric progression with common ratio isa1q. a=first term of geometric progression
P[A]=0.25×0.750.9375=0.20
Hence, answer is
P[A]=0.20

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