Unformatted text preview: q=0.1 .What is the minimum value of k in order to have an expected profit of $1 per manufactured circuit? (3) (20 points) The CDF of a continuous random variable X is ⎪ ⎩ ⎪ ⎨ ⎧ ≥ < ≤ − + − < = 1 1 1 1 2 / ) 1 ( 1 ) ( x x x x x F X Find (a) (8 point) ) ( x f X (b) (6 point) ] [ X E (c) (6 point) ] [ X VAR (4) (30 points) A continuous random variable X has PDF ⎩ ⎨ ⎧ ≤ ≤ − = otherwise x x f X 3 1 4 / 1 ) ( Define the random variable Y by Y=h(X)=X 2 . Find (a) (5 points) E[X] (b) (5 points) VAR[X] (c) (5 points) h(E[X]) (d) (5 points) E[h(X)] (e) (5 points) E[Y] (f) (5 points) VAR[Y] (5) (20 points) The PDF of a random variable X is ⎩ ⎨ ⎧ ≥ = − otherwise x e x f x X ) 2 / 1 ( ) ( 2 / Find a. (5 points) ] 2 1 [ ≤ ≤ X P b. (5 points) F X (x) c. (5 points) E[X] d. (5 points) VAR[X]...
View
Full Document
 Fall '08
 WOODS
 Probability theory, Discrete probability distribution

Click to edit the document details