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Unformatted text preview: 4.3. EXPECTATION VALUE AND STANDARD DEVIATION 47 or multiplying out
2px |2px = 1
( ψ211 |ψ211 + −ψ211 |ψ21−1 + ψ21−1 | − ψ211 + ψ21−1 |ψ21−1 )
2 or using the orthonormality of ψ211 and ψ21−1 .
2px |2px = 1
(1 + 0 + 0 + 1) = 1.
2 For the state 2py , remember that i comes out of the left side of the inner product as −i:
2py |2py = −i2
ψ211 + ψ21−1 |ψ211 + ψ21−1
2 The rest goes the same way. 4.3 Expectation Value and Standard Deviation 4.3.1 Statistics of a die 18.104.22.168 Solution esda-a Question: Suppose you toss a coin a large number of times, and count heads as one, tails as
two. What will be the expectation value?
Answer: For a fair coin, the probability of heads or tails is the same; each will have a
probability of 50% or 2 . So the expectation value is 1 × 1 + 2 × 2 = 1.5. This will be the
average value you obtain in a large number of throws. 22.214.171.124 Solution esda-b Question: Continuing this example, what will be the maximum deviation?
Answer: If you throw a 1, the deviation is |1 − 1.5| or 0.5. If you throw a 2, the deviation is
|2 − 1.5|, also 0.5. So the maximum deviation is 0.5. ...
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.
- Fall '11