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

2. 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.
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3. 2. Let X be N(1000, s2 = 20). Find Pr(X < 1024 | X > 961).
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4. 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).
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5. 4. Let X be U(0, 10). Plot fX(x| X > 5). Find Pr(X >7|X > 5).
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6. _______________________________________________
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).
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7. 6. X: N(1, s2 = 9); y = 2, x  4 -1, x < 4 fY(y) = ? E(Y) = ?
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8. 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.
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9. _______________________________________________
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).
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10. 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).
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