3. A sensor network consists of a large number of microprocessors spread out ove

Question

3. A sensor network consists of a large number of microprocessors spread out over an area, in communication with each other and with a base station. In certain network, the probability that a message will fail to reach the base station is 0.005. Assume that during a particular day 1000 messages are sent. probsblit's.halsauethaduringa particula day a. What is the probability that exactly three of the b. What is the probability that fewer than 994 of the c. What is the mean number of messages that fail to d. What is the standard deviation of the number of messages fail to reach the base station? messages reach the base station? reach the base station? messages that fail to reach the base station?

Explanation / Answer

Given that,

Probability that a message will fail to reach the base station is 0.005, Let us assume it as p(fail)=0.005.

Number of messages sent on that particular day= 1000.

In the given question such, a message can either succeed in reaching the base station or it will fail, there are only 2 possible outcomes, such experiments are called as Binomial experiments, other example of Binomial experiments are Coin flip.

Some features of binomial experiment are:

The binomial probability of r success in an experiment with ‘P’ as the proability of each success and ‘n’ trails is = nCr * Px *(1-P)n-r

P(X=3)=1000C3 *(0.005)3*(1-0.005)997=0.1403028 (Answer)

P(X>6)=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6))

=1-((1000C0*0.0050*0.9951000)+(1000C1 * 0.005*0.995999)+ (1000C2 * 0.0052*0.995998)+ (1000C3 * 0.0053*0.995997)+ (1000C4* 0.0054*0.995996)+ (1000C5 * 0.0055*0.995995)+ (1000C6 * 0.0056*0.995994))

=(1-(0.006653969+0.03343703+0.08392862+0.1403028+0.175731+0.1759076+0.1465897))

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