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gavmur [86]
3 years ago
11

Suppose calls are arriving at a telephone exchange at an average rate of one per second, according to a Poisson arrival process.

Find: a) the probability that the fourth call after time t = 0 arrives within 2 seconds of the third call; b) the probability that the fourth call arrives by time t = 5 seconds; c) the expected time at which the fourth call arrives.
Mathematics
1 answer:
antoniya [11.8K]3 years ago
5 0

Answer:

Explanation has been given below

Step-by-step explanation:                    

a) inter arrival times are exponentially distributed with mean 1/n , where n = rate = 1/sec.                                                                              

  probability distribution function is F(t)=n*exp(-n*t).  

reference to any kth packet and the (k-1)th packet

the answer is = integration of F(t).dt with limits 0 to 2 = 1 - exp(-2*n) = 1 - exp(-2)  

b)  t=5 , P(q) = exp(-5)*(5)^q/factorial(q)  

probability of fourth call within t=5 seconds is =  

that is P(4)   P(5)   ......  = 1 - ( P(0)   P(1)   P(2)   P(3) ) ;  put the values and get the answer.  

c) number of calls/rate =  4/n = 4 seconds

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3 0
1 year ago
I’ll mark you Brainly-ist if you’re correct.
drek231 [11]

Answer:

log5 19 - log5 x

Step-by-step explanation:

log5 19/x

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log5 19 - log5 x

5 0
3 years ago
What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?
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Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

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3 years ago
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Answer:

.20

Step-by-step explanation:

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Suppose that 90% of bolts and 85% of nails meet specifications. One bolt and one nail are chosen independently. What is the prob
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Answer:

76.5% probability that both meet specifications.

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Step-by-step explanation:

We have these following probabilities:

A 90% probability that a bolts meets specifications

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We multiply both probabilities:

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76.5% probability that both meet specifications.

What is the probability that neither meets specifications?

A 10% probability that a bolts does not meet specifications

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