Question

Assume a Poisson random variable has a mean of 10 successes over a 120-minute period.

**a.** Find the mean of the random variable, defined
by the time between successes.

**b.** What is the rate parameter of the appropriate
exponential distribution?

**c.** Find the probability that the time to
success will be more than 54 minutes

Answer #1

Assume a Poisson random variable has a mean of 10 successes over
a 120-minute period.
A. Find the probability that the time to success will be more
than 54 minutes
B. Find the mean of the random variable, defined by the time
between successes.
C. What is the rate parameter of the appropriate exponential
distribution?

Assume a Poisson random variable has a mean of 10 successes over
a 120-minute period.
a. Find the mean of the random variable, defined
by the time between successes.
b. What is the rate parameter of the
appropriate exponential distribution? (Round your answer to
2 decimal places.)
c. Find the probability that the time to
success will be more than 54 minutes. (Round intermediate
calculations to at least 4 decimal places and final answer to 4
decimal places.)

Assume a Poisson random variable has a mean of 4 successes over
a 128-minute period.
a. Find the mean of the random variable, defined
by the time between successes.
b. What is the rate parameter of the
appropriate exponential distribution? (Round your answer to
2 decimal places.)
c. Find the probability that the time to
success will be more than 60 minutes. (Round intermediate
calculations to at least 4 decimal places and final answer to 4
decimal places.)

Assume a Poisson random variable has a mean of 8 successes over
a 128-minute period.
a. Find the mean of the random variable, defined by the time
between successes.
b. What is the rate parameter of the appropriate exponential
distribution? (Round your answer to 2 decimal places.)
c. Find the probability that the time to success will be more
than 55 minutes. (Round intermediate calculations to at least 4
decimal places and final answer to 4 decimal places.)

The exponential distribution is frequently applied
to the waiting times between successes in a Poisson
process. If the number of calls received per hour
by a telephone answering service is a Poisson random
variable with parameter λ = 6, we know that the time,
in hours, between successive calls has an exponential
distribution with parameter β =1/6. What is the probability
of waiting more than 15 minutes between any
two successive calls?

Consider a customer arrival process that is a Poisson process.
To find the probabilities described below, which of the following
random variable selections (as Poisson, Exponential or k-Erlang) is
correct?
to find the probability that the time between the 2nd and 3rd
customer arrivals is 5 minutes, use a k-Erlang random variable with
k>1
to find the probability that 10 customers arrive during a
30-minute period, use a k-Erlang random variable
to find the probability that the total time elapsed...

If random variable X has a Poisson distribution with
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find P(X>8) Round to 4 decimal places.

The number of automobiles entering a tunnel per 2-minute period
follows a Poisson distribution. The mean number of automobiles
entering a tunnel per 2-minute period is four. (A) Find the
probability that the number of automobiles entering the tunnel
during a 2- minute period exceeds one. (B) Assume that the tunnel
is observed during four 2-minute intervals, thus giving 4
independent observations, X1, X2, X3, X4, on a Poisson random
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Let the mean success rate of a Poisson process be 12 successes
per hour.
a. Find the expected number of successes in a 19
minutes period. (Round your answer to 4 decimal
places.)
b. Find the probability of at least 2 successes in
a given 19 minutes period. (Round your answer to 4 decimal
places.)
c. Find the expected number of successes in a two
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places.)
d. Find the probability...

Every day, patients arrive at the dentist’s office. If the
Poisson distribution were applied to this process:
a.) What would be an appropriate random variable? What would be
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b.)If the random discrete variable is Poisson distributed with λ
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distribution has x = minutes until the next arrival, identify the
mean of x and determine the following:
1. P(x less than or equal to 6)...

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