Question

Draw an uncertain event that is characterized by an exponential distribution.

Answer #1

**Exponential
Distribution:**

*The exponential distribution is the
probability distribution that describes the time
between events in a Poisson point process, i.e., a process in which
events occur continuously and independently at a constant average
rate.*

**Example of
Exponential Distribution:**

*You observe the number of calls that arrive each day over a
period of a* *year,* *and note that the arrivals
follow a Poisson distribution with an average of 3 per
day.*

*Let T be the waiting time between calls.*

*Then T will follow an exponential distribution.*

Draw an uncertain event that is characterized by the
discrete uniform distribution with four potential outcomes (A, B,
C, D).

Suppose that the time between successive occurrences of an event
follows an exponential distribution with mean number of occurrences
per minute given by λ = 5. Assume that an event occurs. (A) Derive
the probability that more than 2 minutes elapses before the
occurrence of the next event. Derive the probability that more than
4 minutes elapses before the occurrence of the next event. (B) Use
to previous results to show: Given that 2 minutes have already
elapsed, what is...

The exponential distribution
Consider the random variable X that follows an exponential
distribution, with μ = 40.
The standard deviation of X is σ = a. 40 b.0.0006 c. 6.321 d.
0.0250 .
The parameter of the exponential distribution of X is λ = a.40
b. 0.0250 b. 6.321 d. 0.0006 .
What is the probability that X is less than 27?
P(X < 27) = 0.2212
P(X < 27) = 0.5034
P(X < 27) = 0.4908
P(X < 27)...

Compute and compare λ(t) for exponential,
Weibull distribution, and Gamma distribution.

1) EXPLAIN STANDARD DENOTATION OF EXPONENTIAL DISTRIBUTION

Derive the cdf for an exponential distribution with parameter
λ.

Data collected at an airport suggests that an exponential
distribution with mean value 2.855 hours is a good model for
rainfall duration.
What is the probability that the duration of a particular
rainfall event at this location is at least 2 hours? At most 3
hours? Between 2 and 3 hours?
What is the probability that rainfall duration exceeds the mean
value by more than 2 standard deviations?

Write out the poisson distribution in exponential family
form.

Use
Laplace inversion formula to find the cdf of exponential
distribution.

Suppose that X follows an exponential distribution
?(?) = {??
-?? 0,,
? ? > ≤ 0 0
And let’s assume random variable ? = 2? + 4 find the expected
value of Y. (?[?])

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