sta4321-9 - Mean and Variance of Discrete Random Variables...

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Mean and Variance of Discrete Random Variables
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Expected Value Variance and Standard Deviation Practice Exercises Expected Value of Discrete Random Variable Suppose you and I play a betting game: we Fip a coin and if it lands heads, I give you a dollar, and if it lands tails, you give me a dollar. On average, how much am I expected to win or lose? expected winnings =( - 1 ) ± 1 2 ² ³ ´µ win -$1 half the time +( 1 ) ± 1 2 ² ³ ´µ win $1 half the time = 0 Arthur Berg Mean and Variance of Discrete Random Variables 2/ 12
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Expected Value Variance and Standard Deviation Practice Exercises Expected Value of Discrete Random Variable Suppose you and I play a betting game: we Fip a coin and if it lands heads, I give you a dollar, and if it lands tails, you give me a dollar. On average, how much am I expected to win or lose? expected winnings =( - 1 ) ± 1 2 ² ³ ´µ win -$1 half the time +( 1 ) ± 1 2 ² ³ ´µ win $1 half the time = 0 Arthur Berg Mean and Variance of Discrete Random Variables 2/ 12
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Expected Value Variance and Standard Deviation Practice Exercises Expected Value of Discrete Random Variable Suppose you and I play a betting game: we Fip a coin and if it lands heads, I give you a dollar, and if it lands tails, you give me a dollar. On average, how much am I expected to win or lose? expected winnings =( - 1 ) ± 1 2 ² ³ ´µ win -$1 half the time +( 1 ) ± 1 2 ² ³ ´µ win $1 half the time = 0 Arthur Berg Mean and Variance of Discrete Random Variables 2/ 12
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Expected Value Variance and Standard Deviation Practice Exercises Expected Value of Discrete Random Variable Suppose you and I play a betting game: we Fip a coin and if it lands heads, I give you a dollar, and if it lands tails, you give me a dollar. On average, how much am I expected to win or lose? expected winnings =( - 1 ) ± 1 2 ² ³ ´µ win -$1 half the time +( 1 ) ± 1 2 ² ³ ´µ win $1 half the time = 0 Arthur Berg Mean and Variance of Discrete Random Variables 2/ 12
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Expected Value Variance and Standard Deviation Practice Exercises Expected Value of Discrete Random Variable Suppose you and I play a betting game: we Fip a coin and if it lands heads, I give you a dollar, and if it lands tails, you give me a dollar. On average, how much am I expected to win or lose? expected winnings =( - 1 ) ± 1 2 ² ³ ´µ win -$1 half the time +( 1 ) ± 1 2 ² ³ ´µ win $1 half the time = 0 Arthur Berg Mean and Variance of Discrete Random Variables 2/ 12
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Expected Value Variance and Standard Deviation Practice Exercises Defnition oF Expected Value oF a Discrete Random Variable Defnition The expected value of a discrete random variable X with probability distribution p ( x ) is given by E ( X ) ± μ = ± x xp X ( x )( ± ) where the sum is over all values oF x For which p X ( x ) > 0. Note that in order For ( ± ) to exist, the sum must converge absolutely; that is ± x | x | p X ( x ) < ( ± ) IF ( ± ) does not hold, we say the expected value oF X does not exist.
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sta4321-9 - Mean and Variance of Discrete Random Variables...

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