THE UNIVERSITY OF TEXAS AT DALLAS



Practice Problems Set #3[1] The joint PMF of two discrete random variables X and Y isPX,Yx,y=cxy, x= -3,1,2,y=-1,10 , otherwise Find the(i) value of c, (ii) P[X2+Y2<10],(iii) expected value of (X2+Y2),(iv) correlation coefficient of X and Y, and the(v) PMF of W= (X2+Y2)[2] X and Y are two continuous random variables with joint pdf fX,Yx,y=cxy, 0≤x≤5,0≤y≤30 , otherwise Find the(i) value of c, (ii) expected value of X when Y=1, and (iii) correlation coefficient of X and Y.(iv) Are X and Y independent?[3] X and Y are two continuous random variables with joint pdf fX,Yx,y=cxy, 0≤x≤2,x≤y≤2x0 , otherwise Find the(i) value of c, (ii) expected value of X when Y=1, and (iii) correlation coefficient of X and Y.[4] X and Y are two continuous random variables with joint pdf fX,Yx,y=c, x2+y2≤4,y>0,x>00 , otherwise Find the(i) value of c, (ii) pdf of Z=X2+Y2.[5] X is uniform from 0 to 1. For any given X=x, Y is uniform from 0 to x. Find the pdf of X when Y=0.5[6] X and Y are jointly Gaussian. The mean and variance of X is 2 and 9, while the mean and variance of Y are -1 and 4. If the correlation coefficient of X and Y is -0.5, find the probability that X>3 when Y=1.[7] Consider a set of independent and identically distributed random variables, (i=1,2,…,200). It is known that each random variable in the set is uniformly distributed between -1 and 3. Clearly stating any assumptions, find the approximate probability . [8] X is a Gaussian random variable with variance 0.25. The mean of X is estimated by taking the sample mean of independent samples of X. If the mean needs to be estimated within 0.01 from the actual mean with a confidence coefficient of 0.99, find the minimum number of samples needed in the estimation. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download