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Statistics: Uniform and Poisson Distributions

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Questions and Answers

What is the correct expression for the uniform density function if the arrival range is between 120 and 140 minutes?

$f(x)=1/200$ when $120 \le x \le 140$
$f(x)=1/120$ when $120 \le x \le 140$
$f(x)=1/20$ when $120 \le x \le 140$ (correct)
$f(x)=1/140$ when $120 \le x \le 140$

Under which condition is it appropriate to use the Poisson distribution?

The events are occurring at a constant rate.
The probability of multiple events occurring at the same instant is significant.
The average of the random variables can be accurately predicted.
The probability that two events coincide is zero. (correct)

Which formula is correct for calculating the mean in an exponential distribution?

$1/(h+a)$
$1/(h-a)$ (correct)
$1/(h)$
$1/(h+a^2)$

If the range for a uniform distribution is from 120 to 140 minutes, what is the value of the density function?

<p>$1/20$ (D)</p> Signup and view all the answers

Which statement accurately describes a property of the Poisson distribution?

<p>The number of occurrences is not fixed over a time interval. (A)</p> Signup and view all the answers

Flashcards

Uniform Density Function

A function where probabilities are equally likely within a specific range.

Poisson Distribution Conditions

Situations where events occur independently over time or space.

Mean of Exponential Distribution

The average outcome in an exponential distribution, calculated as 1/(h-a).

Conditions for Poisson Distribution

Requires the average rate to be constant and events are independent.

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Continuous Uniform Distribution

A type of distribution where all outcomes are equally likely in a defined interval.