ECE 450 Mid-semester Review/Practice HW Requests: ____________________ ________________________________

1. An archer aims at the bullseye (center) of a circular target of radius 10”. His aimpoint errors in the horizontal and vertical directions are each N(0, s2 = 4). Find the probability that he misses the circular target completely. _______________________________________________

2. Let X be N(1000, s2 = 20). Find Pr(X < 1024 | X > 961). _______________________________________________

3. Consider the experiment of rolling a single die 3. Consider the experiment of rolling a single die. Let X be the number showing on the die. Plot: fX(x | X > 3) and FX(x | X > 3). _______________________________________________

4. Let X be U(0, 10). Plot fX(x| X > 5). Find Pr(X >7|X > 5). _______________________________________________

_______________________________________________ 5. Consider a uniform RV, X: U(-10, 10) Suppose X is input to a hard-limiter, with transfer characteristic: 5 -5 x y Find fY(y). -5 5 _______________________________________________

6. X: N(1, s2 = 9); y = 2, x  4 -1, x < 4 fY(y) = ? E(Y) = ? _______________________________________________

7. A Gaussian random current has mean 1A and standard deviation 4A 7. A Gaussian random current has mean 1A and standard deviation 4A. It is flowing through a resistance of 10W. Find the mean power dissipated by the resistor. _______________________________________________

_______________________________________________ 8. Consider the pair of RV’s X and Y based on the experiment of tossing a single die: Die 1 2 3 4 5 6 X Y Graph f(x, y). Find FX(1, 0). _______________________________________________

9. RV’s X and Y have joint pdf: f(x, y) = 2exp(-(x+2y)) 9. RV’s X and Y have joint pdf: f(x, y) = 2exp(-(x+2y)). Find (a) the correlation coefficient, r, for the two RV’s; and (b) E(X) and E(Y) and E(XY). _______________________________________________