Continuous RV MCQs

If in a manufacturing plant, X and Y are two independent machines with a and b representing their respective efficiencies, then Var(aX - bY ) =

• Var(aX - bY) = a^2 * Var(X) + b^2 * Var(Y)

• Var(aX - bY) = a * Var(X) + b * Var(Y)

• Var(aX - bY) = a^2 * Var(X) - b^2 * Var(Y)

• Var(aX - bY) = a * Var(X) - b * Var(Y)

If a company's sales distribution function is F for the random variable X and if a < b, then the probability that the sales fall between a and b is given by

• F(a) - F(b)

• F(a) + F(b)

• F(a) * F(b)

• F(b) - F(a)

A survey is being conducted to measure the income levels of individuals. Which of the following best describes a variable that can assume any possible value between two points?

• discrete variable

• categorical variable

• nominal variable

• continuous variable

Family size can be represented by the random variable x. determine the
average family size

x 2 3 4 5

P(x) 0.17 0.47 0.26 0.10

• 3.23
• 1.98
• 4.12
• 2.75

If a random variable X represents the number of hours a student studies per day and Y represents the number of hours a student is expected to study, what is the expected value of the difference between X and the mean (μ)?

• 1

• 2

• 0.1

• 0

If the exponential distribution is given as f(x)=ke^{-kx}, x>0, then the mean of the distribution is

• 1/k

• k

• e^k

• e^{-k}

If the exponential distribution is given as f(x)=ke^{-x/k}, x>0, then P(X>k)=

• e^{-1}

• e^{-2}

• -1

• 1