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Explain the concept of discrete random variables.
Discrete random variables are countable and can only take on a finite or countably infinite number of values. Examples include the number of heads in coin flips.
Explain the concept of continuous random variables.
Continuous random variables are measurable and can take on any value within a given range. Examples include height or time.
Explain the importance of the sum of probabilities in a probability distribution.
The sum of all probabilities in a probability distribution must always equal 1.0, representing all possible outcomes.
Explain the concept of skewness in a distribution.
Skewness refers to the asymmetry of a distribution. A right-skewed distribution has a long tail to the right, while a left-skewed distribution has a long tail to the left.
Explain the importance of understanding the shape of a distribution.
Understanding the shape (symmetry, peaks, skewness) helps in interpreting the data and choosing appropriate statistical methods.
What are the differences between discrete and continuous random variables?
Discrete: Countable, finite/countably infinite values | Continuous: Measurable, any value within a range
What are the differences between a symmetric and a skewed distribution?
Symmetric: Evenly distributed around the center | Skewed: Values concentrated on one side, long tail on the other
What are the differences between single-peaked and double-peaked distributions?
Single-Peaked: One dominant group of values | Double-Peaked: Two distinct groups of values
What is the definition of a random variable?
A variable whose value is a numerical outcome of a random phenomenon.
What is a discrete random variable?
A random variable that can only take on a finite or countably infinite number of values.
What is a continuous random variable?
A random variable that can take on any value within a given range.
What is a probability distribution?
A function that tells you the probability of each possible value a random variable can take.
Define symmetry in a probability distribution.
Values are evenly distributed around the center.