ECE302 Quiz-06

What is the cumulative distribution function (CDF) of a continuous random variable X defined

• F_X(x) = P[X = x]

• F_X(x) = P[X ≥ x]

• F_X(x) = P[X ≤ x]

• F_X(x) = P[X < x]

Which property does the CDF of a random variable always satisfy?

• It is non-increasing

• It is non-decreasing

• It always equals 0 at infinity

• It must be left-continuous

How is the probability density function (PDF) related to the CDF?

• The CDF is the derivative of the PDF

• The PDF is the integral of the CDF

• The PDF is the derivative of the CDF

• The CDF is always equal to the PDF

What is the median of a random variable X defined as using the CDF?

• F_X(c) = 0.25

• F_X(c) = 0.75

• F_X(c) = 0.5

• F_X(c) = 1

How is the mode of a continuous random variable X determined?

• It is the value that maximizes the CDF

• It is the value that minimizes the PDF

• It is the value that maximizes the PDF

• It is the median value of the data set

How can the mean of a positive continuous random variable X be computed using the CDF?