STAT01

• What does a random variable represent?

  A numerical value associated with outcomes
• When is a random variable considered discrete?

  If it has a finite or countable number of outcomes
• What defines a continuous random variable?

  It has uncountable outcomes on a number line
• Is the distance your car travels on a tank of gas discrete or continuous?

  Continuous random variable
• Is the number of students in a statistics class discrete or continuous?

  Discrete random variable
• What is the sample space when rolling two dice?

  36 sample points
• How do you construct a discrete probability distribution?

  List values with their probabilities
• What must the probabilities in a discrete probability distribution satisfy?

  Each probability is between 0 and 1
• What is the sum of all probabilities in a discrete probability distribution?

  It must equal 1
• What are the steps to construct a discrete probability distribution?

  1. Make a frequency distribution
  2. Find the sum of frequencies
  3. Calculate probabilities by dividing frequency by total
  4. Check probabilities are between 0 and 1, and sum is 1
• What is the probability of landing on 1 in a spinner divided into two sections?

  0.25
• What is the probability of landing on 2 in a spinner divided into two sections?

  0.75
• What is the probability of the sum of two spins being 2?

  0.0625
• What is the probability of the sum of two spins being 3?

  0.375
• What is the probability of the sum of two spins being 4?

  0.5625
• How do you find the mean of a probability distribution?

  • Multiply each outcome by its probability
  • Sum the results
• What is the mean of the probability distribution for the sum of two spins?

  3.5
• How do you find the variance of a probability distribution?

  • Calculate the mean
  • Find the squared differences from the mean
  • Multiply by probabilities and sum
• What is the variance for the two spins?

  Approximately 0.376
• How do you find the standard deviation of a discrete random variable?

  • Take the square root of the variance
• What is the standard deviation of the probability distribution for the sum of the two spins?

  Approximately 0.613
• What is the expected value in a raffle scenario?

  • Calculate gains for each prize
  • Consider the cost of the ticket
• What is the expected value of your gain in the raffle with two prizes?

  Approximately -$1.696
• What are the possible outcomes in the raffle scenario?

  • Winning $100
  • Winning $50
  • Losing $1
• What does X represent in the context of the study material?

  X is the number of Internet line contracts
• What is the probability distribution of the number of new Internet line contracts daily?

  • P(X=5) = 0.2
  • P(X=3) = 0.45
  • P(X=2) = 0.25
  • P(X<2) = 0.25 + P(X=2)
  • P(X≥3) = 0.55
  • P(X>3) = 0.25 + P(X=4)
  • P(X<3) = 0.45
• What is the probability that the company will get exactly 5 contracts in a day?

  0.2
• What is the probability that the company will get exactly 3 contracts in a day?

  0.45
• What is the probability that the company will get exactly 2 contracts in a day?

  0.25
• How do you calculate the probability of getting less than 2 contracts in a day?

  0.25 + P(X=2)
• What is the probability of getting at least 3 contracts in a day?

  0.55
• How do you find the probability of getting more than 3 contracts in a day?

  0.25 + P(X=4)
• What is the probability of getting less than 3 contracts in a day?

  0.45
• What values are provided for the random variable X in the probability distribution table?

  • X values: 1, 4, 7, 10
  • Corresponding probabilities: 3/10, 1/5, 20, 1/20, 2/15, 30, 40, 50, 3/10, 1/2
• What is the average number of credit cards a savings account customer has according to the bank vice president?

  Three credit cards
• What are the mean, variance, and standard deviation for the number of credit cards?

  • Mean (µ) = 1.34
  • Variance (σ²) = 0.9244
  • Standard deviation (σ) = 0.9615
• Is the bank vice president's claim about credit cards correct?

  No, the average is 1 credit card
• What are the mean, variance, and standard deviation for the number of pizzas delivered?

  • Mean = 42.1
  • Standard deviation = 1.1858
• What does the pizza shop owner claim about the number of pizzas delivered in one day?

  45 pizzas were delivered
• Is the pizza shop owner's claim believable based on statistics?

  No, it is biased