9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

Q: LEnd Ale Loplaee trons form for the follwiner funetion flt)= (1ot)

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Q: Determine. '{F}. 4s2 + 3 sF(s) – SF(s) – 2F(s) = - s + 4s

A: Rewrite the given equation.

Q: If X ~ N(5,2). Calculate P(X<6) [Draw a figure]

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Q: 2. Sキ 1 dx 5+x2

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Q: A 2. Find the distance between (-1, -7) and (5, 9). O 2v13 O 2v73 O v22 O 2V5

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Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g.…

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Q: dz 4. Compute where

A: We can solve the problem by residue method

Q: Letfandgbetwomultiplicativefunctionsand∈S.Wehavef◦(g◦F)= (fg)◦F.

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

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Q: Let u (9, 9, 8) and = (-9, -1, - 8). = Find proj, (u). -

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Q: Suppose that x is N(15,4). Find the P(X>11).

A: The random variable X follows normal distribution. The population mean is 15. The population…

Q: Suppose that q 1 is a constant. Calculate the sum n Sn = kqk = q + 2q² + 3q³ +…+nq” k=1

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Q: . Show that p(X) = XP-1 +... +X +1 when p is prime.

A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

Q: Let X~N(10,9). Find P(Z > -2)

A: It is given that, X~N(10,9)

Q: 3. Find the distance between (-1, -7) and (5, 9). O V22 O 2v73 O 2v5 O 2V13

A: The distance between the point (x1,y1) and (x2,y2) is given by D=(x2-x1)2+(y2-y1)2

Q: Compute f. F · dr, where F(x, y) = (8 + 21x², 4xy) and C is a line segment from (0,0) to (1,2). (Use…

A: Given F(x,y)=8+21x2,4xy2        (1) Line segment from (0,0) to (1,2) is y-0=2-01-0(x-0)⇒y=2x…

Q: Suppose X~N(19, 2.5).  Find P(X = 17)

A: Given X~N(19, 2.5)

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Q3// Let x be a r.v having p.m.f X -2 -1 5 P(X) 20 3C 20 C 4C 1) Find the value of C? 2) Find C. d.…

A: The pmf is given as X -2 -1 0 2 3 5 P(X) C 2C 3C 2C C 4C 1. It is known fact that,  ∑ P(X)…

Q: Q2. P(A) = 0.42, P(B|A) = 0.66 and P(B|A’) = 0.25. Find the following – P(A’), P(B’|A), P(B’|A’),…

A: We have given information, P(A)=0.42 PB|A=0.66 P(B|A')=0.25

Q: Determine the length of x = 4(3 + y)* , 1<y<4 %3D

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: 1. [-(p A -q)] V -r

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Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: j+ky-o Find k Iet yco)=lo0 andyc2)=4 3D0

A: Given that y'+ky=0 y(0)=100 and y(2)=4

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

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Q: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

A: Given, x3≡amod p At p=7 We know that suppose p is rational prime p≡1mod 3 then x3≡a mod p is…

Q: Let X N(10, 23). Then P( X< 10) = %3D

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Q: = Suppose (3, −1, −2), = (-1, 1, −4) and w = . 9. 9. v.w= 9. v. v= ū⋅ (v+w)= . 9. (5, 1, 1). Then:

A: For any query with the solution, please ask in the comment box.

Q: () - (" ;')-(,".) Show that: n+1

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Q: 10.

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Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: Find the Polah farm of Z=(-1+)

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Q: ..***a***** . Let x (m, 1,0,-2)", m > 0 and ||x||2 = V30, then Select one: a. 6 b. 7 с. 5 d. 4

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Q: (9) Let P, Q, R be (a) (¬P VQ) (b) (P mathematical statements. Negate the following statements.…

A: