Understanding Random Variables

What is a random variable?

• A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

• A random variable is a type of constant used in equations.

• A random variable is a variable that can only take on one specific value.

• A random variable is a fixed value in a statistical model.

Define a discrete random variable.

• A discrete random variable is a variable that can take on an infinite number of values.

• A discrete random variable can take on any value within a range.

• A discrete random variable is a variable that can only take on negative values.

• A discrete random variable is a variable that can take on a countable number of distinct values.

Define a continuous random variable.

• A continuous random variable is limited to a finite set of outcomes.

• A continuous random variable cannot take values outside of zero.

• A continuous random variable can take any value within a specified range.

• A continuous random variable can only take integer values.

What is the expected value of a random variable?

• The expected value is the average of the highest values only.

• The expected value is the maximum value of the random variable.

• The expected value is the product of all values divided by the number of values.

• The expected value is the sum of all possible values, each multiplied by its probability.

How do you calculate the expected value for a discrete random variable?

• E(X) = Σ [P(x) / x]

• E(X) = Σ [x * P(x)]

• E(X) = x * Σ [P(x)]

• E(X) = P(x) / x

How do you calculate the expected value for a continuous random variable?

• E[X] = x * f(x) + C

• E[X] = ∫ x * f(x) dx

• E[X] = ∫ f(x) dx

• E[X] = Σ x * P(x)

What is the difference between a probability mass function and a probability density function?

• PMF is for discrete variables; PDF is for continuous variables.

• PMF is a graphical representation; PDF is a numerical representation.

• PMF and PDF are the same; they both apply to discrete variables.

• PMF is used for continuous variables; PDF is for discrete variables.

Give an example of a discrete probability distribution.

• Normal distribution

• Poisson distribution

• Exponential distribution

• Binomial distribution

Give an example of a continuous probability distribution.

• Poisson distribution

• Geometric distribution

• Binomial distribution

• Normal distribution

What is the significance of the mean in a probability distribution?

• The mean signifies the expected value and central tendency of a probability distribution.

• The mean is the same as the median in all distributions.

• The mean indicates the spread of the data points.

• The mean represents the maximum value in a distribution.