{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT6_041F10_assn06

MIT6_041F10_assn06 - Massachusetts Institute of Technology...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Problem Set 6 Due October 27, 2010 1. Random variables X and Y are distributed according to the joint PDF ax, if 1 x 2 and 0 y x, f X,Y ( x, y ) = 0 , otherwise . (a) Evaluate the constant a . (b) Determine the marginal PDF f Y ( y ). (c) Determine the conditional expectation of 1 /X given that Y = 3 / 2. (d) Random variable Z is defined by Z = Y X . Determine the PDF f Z ( z ). 2. Let X and Y be two independent random variables. Their probability densities functions are shown below. 1 0.8 f X ( x ) 0.6 0.4 0.2 0 x 1 4 f X ( x ) = 3 (1 x 2 ) −1.5 −1 −0.5 0 0.5 1 1.5 f Y ( y ) 0.8 0.6 0.4 0.2 0 1 3 3 2 0 0.5 1 1.5 2 2.5 3 y Let Z = X + Y . Determine f Z ( z ). 3. Consider n independent tosses of a k -sided fair die. Let X i be the number of tosses that result in i . (a) Are X 1 and X 2 uncorrelated, positively correlated, or negatively correlated? Give a one-line justification.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}