4.9 Combining Random Variables

• Match the type of random variable with its definition:

  Discrete ↔️ Finite or countably infinite values

  Continuous ↔️ Any value within a range
• A continuous random variable can take on any value within a given range of real numbers.
• Subtracting random variables involves finding the difference between their outcomes.
• When subtracting discrete random variables, the new variable is the difference
• What is a random variable categorized as if it can take on a finite number of distinct values?

  Discrete
• What are the two main types of random variables?

  Discrete and continuous
• Match the random variable operation with its outcome for discrete and continuous variables:

  Addition (Discrete) ↔️ Sum of possible values

  Addition (Continuous) ↔️ Range of possible sums
• What is involved when combining random variables?

  Finding the difference
• Match the type of operation with its result for random variables:

  Subtraction of Discrete Variables ↔️ New discrete variable

  Subtraction of Continuous Variables ↔️ New continuous variable
• The process of subtracting random variables depends on whether the variables are discrete or continuous.


  True
• Match the property of expected values with its formula:

  Expected Value of Constant Multiple ↔️ $E(aX) =$$a \cdot E(X)$

  Expected Value of Difference ↔️ $E(X - Y) =$$E(X) - E(Y)$

  Expected Value of Sum ↔️ $E(X + Y) =$$E(X) +$$E(Y)$
• If Var(X) = 9 and Var(Y) = 16, the standard deviation of X + Y is 5.
• Continuous random variables can take on any value within a given range.
• When subtracting discrete random variables, the new variable is the difference of the individual variables.


  True
• What is a random variable?

  Numerical outcome of random phenomenon
• The height of a person is an example of a discrete random variable.

  False
• What happens to the possible values when adding discrete random variables?

  They are summed
• What is the new random variable called when subtracting discrete random variables?

  The difference of outcomes
• What values can Z = X - Y take if X is the number of heads from flipping a coin three times and Y is the number of tails from flipping it twice?

  -2, -1, 0, 1, 2, 3
• The number of correct answers on a quiz is an example of a discrete random variable.

  True
• Discrete random variables are countable.


  True
• If X and Y are discrete random variables, what type is Z = X + Y?

  Discrete
• For discrete random variables, subtracting them results in a new discrete random variable.


  True
• What is the expected value of a random variable called?

  Mean
• What does the expected value of a random variable represent?

  The average value
• A random variable assigns a numerical outcome to each possible result of a random experiment.


  True
• Match the type of random variable with the operation of addition:

  Discrete Random Variables ↔️ Sum of possible values

  Continuous Random Variables ↔️ Range of all sums
• The expected value of a constant multiple of X is equal to the constant multiplied by E(X).
• Random variables are categorized as either discrete or continuous.
• What type of values can a discrete random variable take?

  Whole numbers, integers
• When adding continuous random variables, the new variable represents the sum of the individual random variables' ranges.


  True
• The probabilities of outcomes for subtracting discrete random variables are calculated based on the independence or dependence
• The process of subtracting random variables depends on whether they are discrete or continuous
• The height of a person is an example of a continuous
• The number of cars passing a tollbooth in an hour is an example of a discrete
• The sum of two continuous random variables is always a continuous random variable.


  True
• For continuous random variables, subtracting them results in a new continuous random variable with values being the differences
• In the example provided, subtracting Y from X results in a new variable Z with possible values ranging from -2 to 3.
• The expected value of the sum of two random variables is equal to the sum of their individual expected values.
• When combining independent random variables, the standard deviation of the sum is the square root of the sum of the individual variances.


  True