Grade 1 Mathematics Quiz: Two Dimensional Random Variables

What is a two dimensional random variable?

• A variable that only takes on one value

• A variable that changes over time

• A variable that can take on three different values

• A variable that can take on two different values

Can you give an example of a two dimensional random variable?

• The outcome of rolling a pair of dice

• The height of a building

• The color of a car

• The temperature of a room

How are two dimensional random variables different from one dimensional random variables?

• One dimensional random variables have two dimensions or components

• Two dimensional random variables have two dimensions or components, while one dimensional random variables have only one dimension or component.

• Two dimensional random variables have three dimensions or components

• Two dimensional random variables have negative dimensions or components

What are the possible values of a two dimensional random variable?

• (x, y) where x and y can only be positive integers

• (x, y) where x and y can only be fractions

• (x, y) where x and y can be any real numbers

• (x, y) where x and y can only be negative numbers

How do we represent a two dimensional random variable?

• Using a probability distribution or a joint probability function

• By flipping a coin

• Through a geometric shape

• Using a linear equation

What is the probability distribution of a two dimensional random variable?

• Marginal probability distribution

• Conditional probability distribution

• Independent probability distribution

• Joint probability distribution

How do we calculate the expected value of a two dimensional random variable?

• E(X,Y) = ∑∑ x*y*P(X=x, Y=y)

• E(X,Y) = x*y*P(X=x) * P(Y=y)

• E(X,Y) = x+y*P(X=x, Y=y)

• E(X,Y) = ∑ x*P(X=x) * ∑ y*P(Y=y)

What is the variance of a two dimensional random variable?

• Var(X) = E[(X + μ)^2] + E[(Y + ν)^2] - 2Cov(X,Y)

• Var(X) = E[(X - μ)^2] + E[(Y - ν)^2] + 2Cov(X,Y)

• Var(X) = E[(X - μ)^2] + E[(Y - ν)^2] - 2Cov(X,Y)

• Var(X) = E[(X - μ)^2] - E[(Y - ν)^2] - 2Cov(X,Y)

Can you explain the concept of covariance in two dimensional random variables?

• Covariance measures the degree to which two variables change together.

• Covariance measures the average of two variables

• Covariance measures the maximum value of two variables

• Covariance measures the difference between two variables

How do we calculate the covariance of two dimensional random variables?

• Cov(X, Y) = E[(X - μx)(Y - μy)]

• Cov(X, Y) = E[(X - μx)^2 + (Y - μy)^2]

• Cov(X, Y) = E[X*Y]

• Cov(X, Y) = E[(X + μx)(Y + μy)]