n is a poisson random variable that represents the number of telephone calls processed in telecommunications switch in 10sec. if the call arrival rate is .5 per second. a) what is the probability that there will be no call processed in 10seconds? b) what is the probability that at least 2 calss will be processed in 2 seconds

Respuesta :

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

what is percentage?

A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.

given,

The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.

a)the chance that no call will be handled in 10 seconds is

for 10 sec= λ= 10*0.5 = 5 calls per sec

P(X=0) [tex]e^{-5}[/tex](5)° / 0!

P(X=0)= 0.0067

b) percent of classes will be processed in two seconds at least is

for 2 sec =λ = 0.5 *2 = 1

P(X≥2) = 1- P(X<2)

= 1-[P(X=2) + P(X=1)]

=0.2642

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

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