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Understanding Probability Distributions: Key Concepts and Calculations

Dive into the fundamentals of probability distributions, random variables, means, and standard deviations. Explore calculating probabilities for coin tosses and learn about discrete and continuous variables.

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Understanding Probability Distributions: Key Concepts and Calculations

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  1. 4.1 Probability Distributions • Important Concepts • Random Variables • Probability Distribution • Mean (or Expected Value) of a Random Variable • Variance and Standard Deviation of a Random Variable

  2. 4.1 Probability Distributions • Consider the following experiment: • Suppose we toss a coin three times. • What is the sample space for this experiment? • What is the probability of tossing exactly: 0 tails? 1 tails? 2 tails? 3 tails?

  3. 4.1 Probability Distributions • Terms to know: • A random variable X represents a numerical value associated with each outcome of a probability experiment. • A random variable is discrete if it has a finite or countable number of possible outcomes. • A random variable is continuous if it has an uncountable number of possible outcomes.

  4. 4.1 Probability Distributions • Terms to know: • A discrete probability distribution lists each possible value a random variable can assume, together with its probability. • All probability distributions must satisfy the following two conditions: • The probability of each value of the random variable must be between 0 and 1, inclusive. • The sum of all the probabilities must be 1. #26 p. 198 #28 p. 198

  5. 4.1 Probability Distributions • Discrete probability distribution of our random variable X:

  6. 4.1 Probability Distributions • How do we find the mean and standard deviation of a discrete random variable? In chapter 3, we used the following: Can we still use these formulas?

  7. 4.1 Probability Distributions • Let’s try #31 p. 199 (Camping Chairs)

  8. 4.1 Probability Distributions • #33 p. 199 (Hurricanes)

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