This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: E(X). x f ( x ) x ⋅ f ( x ) 10 0.2 11 0.4 12 0.3 13 0.1 E(X) = μ X = ∑ ⋅ x x f x all ) ( b) Find the variance of X, Var(X). x f ( x ) ( xμ X ) ( xμ X ) 2 ⋅ f ( x ) 10 0.2 11 0.4 12 0.3 13 0.1 Var(X) = 2 X σ = ( ) ∑ ⋅x x f x all 2 X ) ( μ = E [ X μ X ] 2 x f ( x ) x 2 ⋅ f ( x ) 10 0.2 11 0.4 12 0.3 13 0.1 Var(X) = 2 X σ = [ ] 2 all 2 E(X) ) ( x x f x∑ ⋅ = E ( X 2 ) – [ E(X) ] 2 c) Find the standard deviation of X, SD(X). SD(X) = X σ = 2 X σ E ( g (X) ) = ∑ ⋅ x x f x g all ) ( ) ( E ( a ⋅ X + b ) = a ⋅ E ( X ). + b . Var ( a ⋅ X + b ) = a 2 ⋅ Var ( X ). SD ( a ⋅ X + b ) =  a  ⋅ SD ( X ). 3. Suppose E(X) = 7, SD(X) = 3. a) Y = 2 X + 3. Find E(Y) and SD(Y). b) W = 5 – 2 X. Find E(W) and SD(W). 4. Suppose a discrete random variable X has the following probability distribution: P( X = 0 ) = e 2, P( X = k ) = ! 2 1 k k ⋅ , k = 1, 2, 3, … a) Find E ( X ). b) Find Var ( X )....
View
Full Document
 Spring '08
 Kim
 Probability distribution

Click to edit the document details