Discrete Random Variables
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Questions and Answers

A bag contains 3 red balls and 2 blue balls. A person selects 2 balls at random. Let $X$ be the number of red balls selected. What are the possible values of the random variable $X$?

  • {0, 1, 2} (correct)
  • {0, 1, 2, 3}
  • {0, 1}
  • {1, 2}

A fair coin is tossed 3 times. Let $Y$ be the number of tails observed. What are the possible values of the random variable $Y$?

  • {1, 2}
  • {0, 1, 2, 3} (correct)
  • {0, 1, 2}
  • {1, 2, 3}

A store sells smartphones. Let $Z$ be the number of smartphones sold during a day. What are the possible values of the random variable $Z$?

  • All integers greater or equal to zero. (correct)
  • All real numbers greater than or equal to zero.
  • All integers.
  • All positive integers.

A dice is rolled twice. Let $M$ be the maximum of the two numbers that appear. What are the possible values of the random variable $M$?

<p>{1, 2, 3, 4, 5, 6} (A)</p> Signup and view all the answers

A basketball player shoots 5 free throws. Let $K$ be the number of successful shots. What are the possible values of the random variable $K$?

<p>{0, 1, 2, 3, 4, 5} (D)</p> Signup and view all the answers

A botanist counts the number of petals on different flowers in a field. Let $P$ be the number of petals on a randomly selected flower. What type of random variable is $P$?

<p>Discrete, because the number of petals can only take on whole number values. (B)</p> Signup and view all the answers

A quality control inspector measures the weight of cereal boxes coming off a production line. Let $W$ be the weight of a randomly selected box. What type of random variable is $W$?

<p>Continuous, because weight can theoretically take on any value within a range. (A)</p> Signup and view all the answers

An economist tracks the daily exchange rate between the US dollar and the Euro. Let $E$ be the exchange rate (Euros per Dollar) at the end of a trading day. What type of random variable is $E$?

<p>Continuous, because the exchange rate can take on any value within a certain range. (B)</p> Signup and view all the answers

A group of friends count the number of cars that pass by a certain point on a road in an hour. Let $N$ be the number of cars observed. What type of random variable is $N$?

<p>Discrete, because you can only have a whole number of cars. (D)</p> Signup and view all the answers

A meteorologist measures the daily high temperature in a city. Let $T$ be the high temperature on a randomly selected day. What type of random variable is $T$?

<p>Continuous, because temperature can theoretically have any value within a range. (C)</p> Signup and view all the answers

Flashcards

Sample Space

A set of all possible outcomes from a random experiment.

Random Variable

A variable whose value is a numerical outcome of a random phenomenon.

Discrete Random Variable

A random variable that can only take a finite number of values or a countably infinite number of values.

Continuous Random Variable

A random variable that can take any value within a given range or interval.

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Probability Mass Function (PMF)

The probability associated with each possible value of a discrete random variable.

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Study Notes

  • A random variable is a variable whose value is a numerical outcome of a random phenomenon.

  • The possible values of a random variable are the set of all possible outcomes that the random variable can take.

  • Discrete random variables have a countable number of possible values.

  • Continuous random variables have an uncountable number of possible values, typically within a specific range.

Discrete Random Variable Quiz Items

  • Question: A coin is flipped twice. Let X be the number of heads. What are the possible values of X?

    • Answer: 0, 1, 2

  • Question: A die is rolled. Let Y be the number shown on the die. What are the possible values of Y?

    • Answer: 1, 2, 3, 4, 5, 6

  • Question: A bag contains 3 red balls and 2 blue balls. Two balls are drawn without replacement. Let Z be the number of red balls drawn. What are the possible values of Z?

    • Answer: 0, 1, 2

  • Question: A basketball player shoots three free throws. Let W be the number of successful free throws. What are the possible values of W?

    • Answer: 0, 1, 2, 3

  • Question: A survey asks people how many cars they own. Let V be the number of cars owned by a randomly selected person. What are the possible values of V?

    • Answer: 0, 1, 2, 3, ... (non-negative integers)

  • Question: In a game, a player rolls a die. If they roll a 6, they win. Otherwise they lose. Let X be 1 if they win and 0 if they lose. What are the possible values of X?

    • Answer: 0, 1

  • Question: A store counts the number of customers who enter in an hour. Let Y be the number of customers. What are the possible values of Y?

    • Answer: 0, 1, 2, 3,... (non-negative integers)

  • Question: A box contains 5 defective items and 5 working items. You select three items. Let Z be the number of defective items selected. What are the possible values of Z?

    • Answer: 0, 1, 2, 3

  • Question: A student takes a quiz with 5 multiple-choice questions. Let W be the number of questions they answer correctly. What are the possible values of W?

    • Answer: 0, 1, 2, 3, 4, 5

  • Question: Consider repeatedly flipping a coin until heads appears. Let V be the number of flips required. What are the possible values of V?

    • Answer: 1, 2, 3, ... (positive integers)

Continuous Random Variable Quiz Items

  • Question: A random variable X represents the height of a student in inches. What are the possible values of X?

    • Answer: A range of values, e.g., [0, 100] or any reasonable interval of heights.

  • Question: Let Y be the temperature of a room in degrees Celsius. What are the possible values of Y?

    • Answer: A range of values, e.g., [-50, 50] or any reasonable interval of temperatures.

  • Question: Let Z be the time it takes for a light bulb to burn out, measured in hours. What are the possible values of Z?

    • Answer: [0, ∞) all non-negative real numbers

  • Question: Let W be the weight of a randomly selected apple in grams. What are the possible values of W?

    • Answer: A range of values, e.g., [0, 500] or any reasonable interval of weights.

  • Question: Let V be the exact amount of gasoline (in gallons) that a gas pump dispenses. The pump is designed to dispense up to 20 gallons. What are the possible values of V?

    • Answer: [0, 20]

  • Question: The time spent waiting in a queue at a grocery store checkout is represented by the random variable X (in minutes). What are possible values of X?

    • Answer: [0, ∞)

  • Question: The voltage of a battery selected at random is the random variable Y. What are possible values of Y?

    • Answer: An interval, such as [1.3, 1.7] for a nominal 1.5V battery (allowing for some acceptable range).

  • Question: The percentage of impurity in a chemical product is the random variable Z. What are its possible values?

    • Answer: [0, 100]

  • Question: The length of a randomly selected fish in a lake is denoted by W (in centimeters). What are possible values of W?

    • Answer: [0, upper bound], where the upper bound is the maximum possible length for that species of fish.

  • Question: A circle is drawn, and a random point is selected within it. Let V be the distance from the center of the circle to that point. The radius of the circle is 1. What are the possible values of V?

    • Answer: [0, 1]

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Understand discrete random variables with examples. Review possible values from coin flips to dice rolls, and drawing balls. Essential for statistics and probability.

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