THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE351K, Probability and Random Process, Fall 2007 Assignment No. 8; Due Thursday, October 25, 2007 1.For the following joint pmf, find the following. X Y 1 2 -2 3/8 1/8 3 2/8 2/8 (a)Marginal pmf’s, )(xpXand )(ypY(b)Expected values, ][XEand ][YE(c)Variances, ][XVand ][YV(d)Conditional pmf’s, )|(|yxpYXand )|(|xypXY(e)Conditional expectations, ]|[yYXE=and ]|[xXYE=(f)Are Xand Yindependent? (g))3,5.1(−≥≥YXP(h))3|0(=≥YXP(i)Calculate ][XEfrom ]|[yYXE=. (j)Calculate ][YEfrom ]|[xXYE=. (k)Calculate ],[YXCovand YX,ρ.
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