6. Which inequality is graphed on the number line at right? ob -5 -4 -3 -2 -10T23 [A] XS-1 [B] -x<1 [C] -X5-1 [D] -xZ-1 [E] None of these
5. Suppose X ~Exp(A). (a) [5 pts] Show that E(X) 1/A. [Hint: You can directly use the definition and properties of a gamma function.] (b) [5 pts] Prove that P(x >t+ |xs) P(x > t) for s,t>0. [Hint: You can directly use the tail probability P(X > x) = e-k for x > 0.
Let x(t) be the signal with Fourier transform Xjw) shown below x(j) Let Xs(t) be obtained by sampling x(t) with sampling period Td let xdin]- x(nT) for all integer n. Which option is the plot of Xd(e the Fourier transform of xdinj? Instructions: First sketchXs ω which is the Fourier transtorm of xs nt is going to be infinite number of replicas of Sketch on 3 e cas. You need to n he span between heep as he )and Xole...
5. [22] If Xi, X2, and X3 are independent random variables with E(XI) 4, E(X2)-3, E(X3)2, V(X) = 1, V(X:) = 5, V(Xs) = 2, and Y = 2X1 + X2-3X1 (a) Determine E(Y) and V(Y). P(Y > 2.0) and P( 1.3 Y 8.3).
1) TsCl, py 2) xs NH3 ?? 3) xs CH3 4) Ag20, H20
4. (5pts each) For the following reactions, in each box please provide the major products. Xs b. CH xs Br, hv 1) Et-MgBr 2) H30* CAN d. e. xs LAH f. PPhy Ph H
y-y+2 ; eise iflxc4) Output: else System.out.printin(y) 8. int x-5, y-3 if (xs 10) x x-2 else x-x+2; Output: System.out printin(y): 9. int x -8; while (x 0) system, out .printin ("ні") ; output: - 10. int x 5 do ) while (x > 23) System.out println(x): output: 11. int x 25, y 8 System.out.println (x+ y) 12. int [1 arrayi 12, 4, 6, 8, 10) int value 0; for (int a 0; a array1.1ength; a++) Output value + arrayl...
{Exercise 6.27 (Algorithmic)} Consider the following exponential probability density function. f(x) = }e for > 0 a. Which of the following is the formula for P(xs xo)? 1 P(x <=0) = 4- · 2 P(Z 520)=1-4- 3 P(1 520)=1-6-- Formula #2 b. Find P(x s 1) (to 4 decimals). C. Find P(x > 4) (to 4 decimals). 0.1353 d. Find P(x S 5) (to 4 decimals). e. Find P(1 3 x 5) (to 4 decimals).
3) [3 marks] Use a proof by cases that for all real number x, xs]x]. You may need this definition. For any real numbers x, [x]= x, if x2 0, -x, otherwise. 4) [3 marks] Give a direct proof that If x is an odd integer and y is an even integer, then x + y is odd. 5) [3 marks] Give a proof by contradiction for the proposition in Q4, above. That is, give a proof by contraction for...
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5. The values of a variable X are: 1,3,9,5, 4, 2 Compute the following: x3 {X? [(x - 2) XS