Flashcards
Transformations of Discrete Random variables
Cards in this deck (9)
- 1The general result for a discrete random variable X is:E(g(x)) = Σg(xi)pi
- 2x: 2 , 3 , 8 , 10 , 13 P(X=x): 0.2 , 0.25 , 0.32 , 0.13 , 0.1 Find E(2/x)E(2/x) = (2/2 x 0.2) + (2/4 x 0.25) + (2/8 x 0.32) + (2/10 x 0.13) + (2/13 x 0.1)
= 0.446 - 3x: 1 , 3 , 5 P(X=x): 0.6 , 0.3 , 0.1 E(X) = 2 , var(X) = 1.8 Find mean and variance of Y=X+3 via substitutionE(Y) = (1+3)x0.6 + (3+3)x0.3 + (5+3)x0.1
= 5
var(Y) = (1+3)^2 x0.6 + (3+3)^2 x0.3 + (5+3)^2 x0.1 = 26.8
26.8 - 5^2 = 1.8 - 4What transformations effect the mean?All (+ , - , x , / )
- 5What transformations effect the variance?Multiplication and division
- 6For the transformation Y=aX+b , what is: E(Y)E(Y) = aE(X)+b
- 7For the transformation Y=aX+b , what is: var(Y)var(X) = a^2(var(X))
- 8For the transformation Y=aX+b , what is: s.d(Y)s.d(Y) = a x s.d(X)
- 9If E(X) = 9 , var(x) = 25 , what is E(Y) and var(Y) under Y=2X-1 ?E(Y) = 2(9)-1 = 17
var(Y) = 2^2 x (25) = 100
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- Transformations of Discrete Random variables
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- Doc Boff
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