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- Consider a random variable x that follows a uniform distribution, with a = 8 and b = 14. What is the probability that x is less than 13? P(x < 13) = 0.1667 P(x < 13) = 0.41665 P(x < 13) = 0.24999 P(x < 13) = 0.8333 What is the probability that x is between 11 and 12? P(11 ≤ x ≤ 12) = 0.0541775 P(11 ≤ x ≤ 12) = 0.1667 P(11 ≤ x ≤ 12) = 0.06668 P(11 ≤ x ≤ 12) = 0.091685arrow_forwardInverse laplace transform H.w Find the Inverse Laplace t following:- 1- 1 $3/2 S 2- 52 +2 s²+2 3- tan-1 1 S 4- 3 8s-27 4s+12 5- s²+8s+16 6- 1 √2s+3arrow_forward1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by f(x)=4x² (a) Sketch this function on the interval -4л≤x≤4л for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases? (c) Given that g(x): 4x², -arrow_forwardO what is the relationship between ADoMian decomposition method and homo to Py Perturition method. With Prove it? What is the relationship between Variation iteration Metod and the Successive approximate Method With Prove it?arrow_forward5. Consider the matrix 102 A= 440 002 In this question work to 4 decimal places throughout and give your final answer to 3 decimal places. (a) Use 4 iterations of the power method to calculate an estimate of the maximal mag- nitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1) as the initial estimate of the eigenvector. Given that the the inverse of matrix A is 4 0 -4 1 =- -4 1 4 4 0 0 2 (b) Use this matrix to perform 3 iterations of the power method to calculate an estimate of the minimal magnitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1)" as the initial estimate of the eigenvector.arrow_forwardUsing a random sample of 742 TV households, Acme Media Statistics found that 41.1% watched the final episode of "Still Hanging On." a. Find the margin of error in this percent. b. Write a statement about the percentage of TV households in the population who tuned into the final episode of "Still Hanging On." a. The margin of error is ± %. (Do not round until the final answer. Then round to the nearest hundredth as needed.)arrow_forwardxux +yuy =2xy,withu =2 on y = x2arrow_forwardQuestion 2: Let A(G) be the set of all automorphisms of a group G. Prove that if G is a group having only two elements, then A(G) consists only of I. JLarrow_forwardQ Let E be a subset of a spacex thens - prove that: i) E≤ E 2) Eclosed iff E'SE 3 E = EVE' = E° Ud (E).arrow_forwardQuestion 4: Let G be a finite abelian group of order o(G) and suppose the integer n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y". Prove that this mapping is an automorphism.arrow_forwardQ2/ verify that f grad = (h grad f- f grad h) h h₂ where and h are scalar factions. Solve in paperarrow_forwardQuestion 5: Let G be a group, o an automorphism of G, N a normal subgroup of G. Prove that (N) is a normal subgroup of G.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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