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Expected Value. Expected Value - Definition The mean (average) of a random variable.

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Presentation on theme: "Expected Value. Expected Value - Definition The mean (average) of a random variable."— Presentation transcript:

1 Expected Value

2 Expected Value - Definition The mean (average) of a random variable.

3 Expected Value - Definition The mean (average) of a random variable. 1234 0.200.250.400.15

4 Expected Value - Definition 1234 0.200.250.400.15

5 Expected Value - Definition 1234 0.200.250.400.15

6 Expected Value - Definition 1234 0.200.250.400.15

7 Expected Value – Example 2 Compute the expected value for the following random variable 0246810 0.100.150.180.200.230.14

8 Expected Value – Example 2 Compute the expected value for the following random variable 0246810 0.100.150.180.200.230.14

9 Expected Value – Example 2 Compute the expected value for the following random variable 0246810 0.100.150.180.200.230.14

10 Expected Value – Example 2 Compute the expected value for the following random variable 0246810 0.100.150.180.200.230.14

11 Expected Value – Example 2 Compute the expected value for the following random variable 0246810 0.100.150.180.200.230.14

12 Example 3 – Mega Millions Jackpot For the drawing on March 30, 2012, the jackpot was $656 million. Use the probability distribution below to determine the expected value of this game of chance. PrizeProbability Jackpot1 in 175,711,536 $250,0001 in 3,904,701 $10,0001 in 689,065 $1501 in 15,313 $1501 in 13,781 $101 in 844 $71 in 306 $31 in 141 $21 in 74.8 $0

13 Example 3 – Mega Millions Jackpot For the drawing on March 30, 2012, the jackpot was $656 million. Use the probability distribution below to determine the expected value of this game of chance. PrizeProbability Jackpot1 in 175,711,536 $250,0001 in 3,904,701 $10,0001 in 689,065 $1501 in 15,313 $1501 in 13,781 $101 in 844 $71 in 306 $31 in 141 $21 in 74.8 $0 E[X]=$3.92

14 Example 3 – Mega Millions Jackpot For the drawing on March 30, 2012, the jackpot was $656 million. Use the probability distribution below to determine the expected value of this game of chance. PrizeProbability Jackpot1 in 175,711,536 $250,0001 in 3,904,701 $10,0001 in 689,065 $1501 in 15,313 $1501 in 13,781 $101 in 844 $71 in 306 $31 in 141 $21 in 74.8 $0 E[X]=$3.92 Tickets cost $1, because of the large jackpot the expected “winnings” per ticket are $2.92 ($3.92 - $1.00)

15 Assignment 1. Find the expected value for the following variable: 2. A single fair die is tossed once. Let X be the number facing up. What is the expected value of X? 3. In a gambling game a person draws a single card from an ordinary 52- card playing deck. A person is paid $15 for drawing a jack or a queen and $5 for drawing a king or an ace. A person who draws any other card pays $4. If a person plays this game, what is the expected game? 4. Compute the expected value for the sum of tossing two fair 6 sided dies. 1234.4.3.2.1

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