ek 5. Let a = pt¹ …pºk, and b = pf¹ ...pf, where p; are prime numbers, and ei, fi ≥ 0. Show that gcd(a,b) = [[pmin(e,fi).

Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

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Q: Find a 3 x 3 matrix A such that Ax = 9x for all x in R3. A II

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Q: Prove that the following equations are equivalent. Hint: start by parsing out yu into a function of…

A: To prove that the given equations are equivalent, we'll start by expressing as a function of and…

Q: en P(x >4|X

A: Given : Probability,p = 0.5 number of trial,n = 7 Let x be the random variable that…

Q: B. Suppose that y1, Y2, ., YnidN (0, o2). We wish to find the most powerful test for Ho:02 = o3…

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Q: Let G = (Zj0, X10) then o(G) is а. 5 O b. 4 С. 3 O d. 2 О е. 10

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Q: Let v = [1] and let z = [¹] x The Projx is equal to k k [21] where

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Q: Find the yalues of k for which he series conxer ges.

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Q: Which of the following determinations belongs in the indicated cell of the table?     We reject…

A: Type 1 error :- When the Null Hypothesis is true and when we reject it, in that case we have…

Q: , Giran me qiven family of ines for b=0, I, I 3, I6

A: Graph of  y = -2x y = -2x -1 y = -2x +1 y = -2x -3 y = -2x +3 y = -2x -6 y = -2x +6

Q: Suppose that la| = 12. The number of distinct %3D left cosets of in is: 12 O 6 10 2 None of the…

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Q: Consider a random poker hand of 5 cards. Let X be the number of Hearts in this hand, and let Y be…

A: There are  13 hears,  13 diamonds and  26 cards that are neither hearts or diamonds in a deck of 52…

Q: -1 15. Let A = 2 and B = Find X. A. [0 7] c5 기 В. D.

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Q: Frod the averuge vearlue of the durndkam f over Shoe lad eraual [q,9]

A: Given function is fx=9x3. Need to find the average of f on -9,9. The average of the function f on…

Q: Suppose P(A)= 4, P(B)= .5, following: Find the P(ANB) a. b. P(A'nB) с. d. P(A'UB') P(BA)

A: Comments: As per our guidelines we are supposed to answer only first three subparts. Kindly repost…

Q: Let P(E)=0.85, P(F) = 0.23, and P(EUF) = 0.94. Find (a) P(EIF) and (b) P(FIE). (a) P(EIF) = (Type an…

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Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: Let S := [a, b] with a < b. Then Acc(S) = [a,b]. Ja, bl. □R□ none of the previous.

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Q: 8 12 -4 -2 -5 12R 5R 11R 6R 3R 9R P(X=x) Evaluate R OA. 47 Ов. 1/46 OC. 1/40 OD. 40 OE. None of…

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Q: q² – 1 19. Find if p= In dą

A: By means of calculating derivative of any function of a real variable we measure the…

Q: 2.14 Use the identity EijmEkim = daðn – dad to show that a x (b x c) (a c)b- (a b)c. %3D

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Using Eq. 8.1.2 together with the values of D, and D2, we can evaluate D, for // in principle any…

A: Since I have solved similar ones, Let us start finding the pattern.....     The values of D1, D2…

Q: In a random sample of n pairs of values of X and Y,(xi, yj) occurs fij times for i = 1, 2, ... ,r…

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Q: Show that if a, = (a" – B"), where a = (1 + v5)/2 and ß = (1 – V5)/2 , then th An = an-1 + an-2 and…

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Q: 23. Suppose P(A) = .40 and P(B\A) = .3O. What is the ioint probahilitu of A and B? %3D

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Q: 5. Let f(x,y) = 3x, where 0 ≤ y ≤ x ≤ 1. Find the following. a) Cov(x,y) b) The correlation of X and…

A: (a) To find the covariance and correlation of X and Y, we need to calculate the expected values of…

Q: Let E-fr.8.2): os es , 05 25 1,7√25 rs 7). Compute 6.8365-1051090 mit Answer x III. r

A: ∬∫Ey2 e(x2+y2)3= ∫0π∫01∫7z7(r sin θ)2. e(r2)3. r dr dz dθ= ∫0π∫01∫7z7(r3 sin2 θ). e(r6) dr dz dθNow,…

Q: Find LV LV₂ hpæp(¿h+¿x)uis hæ

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Q: 22) let XnN20, 036), iF P(X<W) = 0.05 th the value of wis

A: Given that, X~N(μ=20, σ=0.36) To find the value of W when P(X&lt;W)=0.05

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

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Q: If P(A)=0.508, What is P(A)? Where A' is the complement of A.

A: If P(A) is probability of occurrence of event A Than P(A') is the probability of not occurrence of…

Q: 8. If W = and V =, compute W x V.

A: To compute w*V from the given vectors.

Q: Q.8 Í xPn+1®n+2dx= Evaluate: n+1*n+2° -1

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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