Lesson 2: Probability Distribution of Discrete Random Variable

Probability Distribution of Discrete Random Variables

Definition

• A probability distribution of a discrete random variable is a structured representation that shows:

  • Possible values of the random variable.

  • The probability associated with each value.

• Provides insight into how likely each value of the random variable will occur.

• Total sum of probabilities for all values must equal 1.

• Individual probabilities are within the range of 0 to 1.

Examples of Finding Possible Outcomes

• Outcomes of Rolling a Die:

  • Individual outcomes include 1, 2, 3, 4, 5, 6.

• Two Dice Rolled and Getting a Total Sum of 6:

  • Possible combinations: (1,5), (2,4), (3,3), (4,2), (5,1).

• Getting an Ace from a Deck of Cards:

  • There are 4 aces in a standard deck of 52 cards.

• Probability Case of Children:

  • If a couple has three children, calculate the probability that all are boys:

    • Possible combinations with respect to gender (B for boy, G for girl): BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG.

• Sum of 11 when Rolling Two Dice:

  • Possible combinations: (5,6), (6,5).

Example of Probability Distribution

Coin Toss Example

• Tossing a fair coin 3 times:

  • Possible outcomes:

    • TTT (0 heads)

    • TTH (1 head)

    • THT (1 head)

    • THH (2 heads)

    • HTT (1 head)

    • HTH (2 heads)

    • HHT (2 heads)

    • HHH (3 heads)

• Let X be a random variable representing the number of heads.

• The possible values for X are {0, 1, 2, 3}.

Summary of Key Concepts

• Understanding and calculating probabilities through different scenarios is essential for grasping probability distributions of discrete random variables.