Question

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.)**

Answer #1

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.)

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 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

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?

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
hours 30 minutes period. (Round your answer to 2 decimal
places.)
d. Find the probability...

A random variable X is exponentially distributed with a
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a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
(Round your answer to 2 decimal places.)
b. Compute P(X > 0.25).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(0.14 ≤ X ≤ 0.25).
(Round intermediate calculations to at least 4 decimal
places and final...

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
variable. Find the probability that the number of automobiles
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A random variable X is exponentially distributed with
an expected value of 57.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of
X?
b. Compute P(54 ≤ X ≤ 60).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(45 ≤ X ≤ 69).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal...

If random variable X has a Poisson distribution with
mean =10, find the probability that X is more than the 8. That is,
find P(X>8) Round to 4 decimal places.

A random variable X is exponentially distributed with a
mean of 0.25.
a-1.
What is the rate parameter
?? (Round your answer to 3 decimal
places.)
Rate parameter
?
a-2.
What is the standard deviation
of X? (Round your answer to 2 decimal
places.)
Standard deviation
X
b.
Compute P(X
> 0.34). (Round intermediate calculations to 4 decimal
places and final answer to 4 decimal places.)
P(X > 0.34)
c.
Compute P(0.18 ?
X ? 0.34). (Round...

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