Day3_Feb_23_M360

Day3_Feb_23_M360 - A box contains 4 quarters and 8 dimes....

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A box contains 4 quarters and 8 dimes. Four coins are chosen at random. The random variable, V , represents the total value of the 4 coins chosen. 1. What values can the random variable attain? 2. Construct the probability distribution for V . 3. What is the probability that the value of the coins is less than 75 cents? 4. What amount of money is most likely to be chosen?
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Q (Quarters) Dimes (4- Q ) v (value) P ( V=v ) F(X< x ) 0 4 $0.40 0.1414141 $0.14 1 3 $0.55 0.4525253 $0.59 2 2 $0.70 0.3393939 $0.93 3 1 $0.85 0.0646465 $1.00 4 0 $1.00 0.0020202 $1.00 Sum= 1
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Q (Quarters) Dimes (4- Q ) v (Value) p ( V=v ) F(X< x ) 0 4 $0.40 0.1414141 $0.14 1 3 $0.55 0.4525253 $0.59 2 2 $0.70 0.3393939 $0.93 3 1 $0.85 0.0646465 $1.00 4 0 $1.00 0.0020202 $1.00 1 What is the probability that the value of the coins chosen is $0.55?
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Q (Quarters) Dimes (4- Q ) v (Value) p ( V=v ) F(X< x ) 0 4 $0.40 0.1414141 $0.14 1 3 $0.55 0.4525253 $0.59 2 2 $0.70 0.3393939 $0.93 3 1 $0.85 0.0646465 $1.00 4 0 $1.00 0.0020202 $1.00 Sum= 1 What is the probability that the value of the coins chosen is v ? 4 8 4 12 4 ( ) Q Q C C P V v C - = =
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Q (Quarters) Dimes (4- Q ) v (value) P ( V=v ) 0 4 $0.40 0.1414141 1 3 $0.55 0.4525253 2 2 $0.70 0.3393939 3 1 $0.85 0.0646465 4 0 $1.00 0.0020202 Sum= 1 P(V< v n ) 0.141414 0.593939 0.933333 0.997980 1.000000 1 ( ) n n i i P V v v = = What is the probability that the value of the coins is less than 75 cents? ( 0.75) ( 0.70) 0.93 p V P V < = =
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Quarters Dimes (4-Q) v (value) p ( X=x ) 0 4 $0.40 0.1414141 1 3 $0.55 0.4525253 2 2 $0.70 0.3393939 3 1 $0.85 0.0646465 4 0 $1.00 0.0020202 Sum= 1 P(X< x n ) 0.141414 0.593939 0.933333 0.997980 1.000000 Most likely value of v ?
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This note was uploaded on 05/14/2010 for the course MATH 360 taught by Professor Wallace during the Spring '10 term at SUNY Geneseo.

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Day3_Feb_23_M360 - A box contains 4 quarters and 8 dimes....

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