15 Questions
Which distribution is commonly used to model the time until the next event in a sequence of independent events with a constant average rate?
Exponential Distribution
Which distribution is symmetric and bell-shaped, making it suitable for modeling many natural phenomena?
Normal Distribution
What is the probability density function used to determine probabilities for a continuous random variable?
Probability Density Function
What is the mean of a continuous random variable?
$rac{1}{2}(a + b)$
Which distribution has the property that any linear combination of two independent random variables with this distribution also has this distribution?
Normal Distribution
For what kind of applications would one typically select the Beta Distribution for calculating probabilities?
Modeling variation in the percentage of defective items in a production process
What does a probability density function describe for a continuous random variable?
The probability distribution of the variable
In a histogram, what does the height of each rectangle represent?
The relative frequency of the data values
What does a cumulative distribution function of a standard normal distribution help to calculate?
Probabilities
What does the loading on the beam between points a & b represent when integrating the density function?
The area under the function from a to b
What feature must a probability density function always have?
$f(x) \geq 0$ means that the function is always non-negative
What does a continuous random variable represent?
A variable with uncountably infinite possible values in an interval
What does the number of possible values of a continuous random variable depend on?
The precision of the measurement instrument
What type of distribution does a probability density function describe?
$f(x)$ describes the probability distribution of a continuous random variable
What does a histogram display?
A graphical representation of data showing adjacent rectangles
Test your knowledge of continuous random variables, probability distributions, and their various types such as normal, binomial, poisson, exponential, erlang, gamma, weibull, lognormal, and beta distributions. Learn about probability density functions, cumulative distribution functions, and the mean and variance of continuous random variables.
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