Probability of a Random Variable

Probability of a Random Variable

• This video lesson focuses on computing probabilities related to random variables, using inequality symbols.
• Inequality symbols are used to represent different scenarios when working with probabilities:
  • Less than (<): "fewer than," "below" (This is the correct symbol for "fewer than")
  • Less than or equal to (≤): "at most," "no more than"
  • Greater than (>): "more than," "above" (This is the correct symbol for "more than")
  • Greater than or equal to (≥): "at least," "no less than"
  • Not equal to (≠): "different from," "not"
  • Equal to (=): "exactly"

Example: Car Dealership Sales

• The video provides an example of a car dealership and the probability distribution of cars sold in a given day:
  • Random variable (X): Number of cars sold
  • Probability: Corresponding probability for each value of X
• Calculating Probabilities:*
• P(X ≤ 2): The probability of selling 2 or fewer cars. This involves summing the probabilities of X = 0, X = 1, and X = 2.
• P(X ≥ 7): The probability of selling 7 or more cars. This involves summing the probabilities of X ≥ 7 (X = 7, X = 8, X = 9, X = 10).
• P(1 ≤ X ≤ 5): The probability of selling between 1 and 5 cars (inclusive). Sum the probabilities of X = 1 through X = 5.

Example: Convenience Store Tellers

• The video gives a scenario of the number of tellers busy at a convenience store at 12 noon:
  • Random variable (X): Number of tellers busy.
  • Probability: The probability of a specific number of tellers being busy.
• Calculating Probabilities:*
• P(X = 4): The probability of exactly 4 tellers being busy.
• P(X ≥ 2): The probability of at least 2 tellers being busy.
• P(X < 5): The probability of fewer than 5 tellers being busy.
• P(2 ≤ X < 5): Probability of at least 2 but fewer than 5 tellers being busy.
• P(X ≥ 0): The probability of at least 0 tellers being busy, which is equal to 1 (representing the sum of all probabilities in a discrete probability distribution).

Example: Leche Puto Sales

• Random variable (X): Number of boxes of leche puto sold.
• Probability: Probability distribution for each value of X.
• Calculating Probabilities:*
• P(X ≥ 40): The probability of selling 40 or more boxes.
• P(37 ≤ X ≤ 50): The probability of selling at least 37 but not more than 50 boxes.
• P(X ≤ 50): The probability of selling no more than 50 boxes.