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Chapter 7 Day 2

Chapter 7 Day 2. Warm - Up. A coin is tossed 4 times. Let X be the number of heads. The table below shows the probability distribution for X. A. Does this represent a legitimate probability distribution? Why or why not? B. Find P(X ≥ 2) C. Find P(X ≥ 1) D. Find P(X ≠ 3). Homework Solutions.

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Chapter 7 Day 2

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  1. Chapter 7 Day 2

  2. Warm - Up • A coin is tossed 4 times. Let X be the number of heads. The table below shows the probability distribution for X. • A. Does this represent a legitimate probability distribution? Why or why not? • B. Find P(X ≥ 2) • C. Find P(X ≥ 1) • D. Find P(X ≠ 3)

  3. Homework Solutions 1. A) 1/3 B-C) Individual answers 2. Done in class 3. A) 1% B) sum = 1 C) 0.94 D) 0.86 E) 0.06 4. A) 0.4 B) 0.6 C) 0.2 D) 0.1 E) 0.487 F) 0.49 G) 0.73 H) 0.73 I) 0.2 J) 0.5 K) 0 5. B) 1/36 D) 2/9 E) 5/6 6. Done in class 7. A) .752 B) yes, sum = 1 C) 0.017 D) 0.024 E) 0.931

  4. Mean of a Random Variable • We use the Greek letter μ (mu) • More specifically we will be talking about the mean of X, so we use μx. • The mean of a random variable is also called the expected value of X.

  5. Mean of a Discrete Random Variable • Suppose that X is a discrete random variable whose distribution is • To find the mean of X, multiply each possible value by its probability, then add all the products:

  6. Example • Recall the example we looked at yesterday of the distribution of the size of households according to Census Bureau studies: • Find the mean size of an American household.

  7. Law of Large Numbers • Draw independent observations at random from any population with finite mean μ. Decide how accurately you would like to estimate μ. As the number of observations drawn increases, the mean of the observed values eventually approaches the mean μ of the population as closely as you specified and then stays that close.

  8. Variance of a discrete random variable • Suppose X is a discrete random variable whose distribution is • And that μ is the mean of X. The variance of X is: • The standard deviation of σX of X is the square root of the variance.

  9. Example • In 1964, New Hampshire started the lottery fad. In the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont the participant picks a three-digit number; the state chooses a three-digit winning number at random and pays you $500 if the number is chosen. Let X be the amount of money you win. Show the probability distribution of X. • Is this a legitimate probability distribution? • Find the mean μX • Find the standard deviation σX

  10. Example • Natalie sells Bean Bag Chairs at the local Pack ‘n Swap. The table below shows the distribution of the number of bean bag chairs sold per day. • Is this a legitimate probability distribution? • Find the mean μX for the number of bean bag chairs sold per day. • Find the standard deviation.

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