ECE302 Quiz-05

What is the key difference between a PMF and a PDF?

• PMF is for continuous variables, PDF is for discrete variables

• PMF sums probabilities, PDF integrates probabilities

• PMF and PDF are identical concepts

• PMF measures length, PDF measures area

Which of the following properties must a probability density function (PDF) satisfy?

• Non-negativity and the total area under the curve equals 1

• Must be below 1 for all x-values

• Must be a discrete function

• Must always be continuous

How is the probability of an interval [a, b] determined for a continuous random variable with a PDF f_X(x)?

• By summing f_X(x) over the interval

• By differentiating f_X(x) at points a and b

• By integrating f_X(x) from a to b

• By multiplying f_X(a) and f_X(b)

What is the definition of the expectation of a continuous random variable X?

• E[X] = Σx * P(X = x)

• E[X] = ∫ x dx

• E[X] = ∫ x fX(x) dx

• E[X] = ∫ fX(x) dx

Which of the following properties is true about expectation?

• E[aX + b] = aE[X] + b

• E[aX] = a + E[X]

• E[X + a] = aE[X]

• E[X] does not change if X is multiplied by a scalar

What is the variance of a continuous random variable X defined as?

• Var[X] = E[X]

• Var[X] = E[X²] - μ

• Var[X] = E[(X - μ)²]

• Var[X] = E[X] + μ²