16.9 a) Show that an element a E(Z,,, O) is a unit iff (a,n) = 1.

Q: s.if {() - % q S.t OSagi0, what is me au sf X ? 50 100 4) 667 c) so d) 10

A: We have given that  Pdf of X is f(x)=(x/50)  , 0≤x≤10

Q: Write the following equation in index form V(div v)+u x (vxw)=p(c®b)a VX W

A:

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: If A₁, A, E and P(A) = P₁, P(A)= P₂, show that P(A₁4₂)≥ 1- P₁ - P₂. (Hint: Use DeMorgan's Law (44₂)…

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Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: Find the values of (A² E¯') u̟ and (A² u,)(E-u). Are they equal.

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Q: Using Boole's Rule, Evaluate (x² + 3y²)dxdy

A: Given:                ∫02∫0yx2+3y2dxdy To do: Evaluate the integral using Boole's rule.

Q: Let a,b,c eZ. If a|b and a |c then a' |(b² =c² ). nsi2

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Q: 5. If x is an integer, then x' 2x. b d a C 6. There exists a real number x such that x'= x . FL

A: we can solve this problem using some basic properties of integers and real number.

Q: 200 ra, is 25a 200 200 Let (1+ x+ x*) = Ïq,x and a = Ea, , then value of

A: We will use basic trics to arrive at the solution

Q: If the characteristic function of a RV X is f,(@) and if Y = aX + b, then O,(@) = ibo e

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Q: f A is a 2 x 2 with det(A) = 5, then det(4A-1) = %3D 80 -) 20 16 5

A: We have to choose the correct answer from the options according to the given condition

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

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Q: 2.6.49 9- Use - o or 0o where appropriate = JO au pue ane uouny upeo pug (B)-20) (X u O) JAIR-10)

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Q: If E, and E2 are measurable then (E,UE,) is not measurable .

A:

Q: if zi = ayi for i=1,2,...,n, show that z=ay

A: Here we have given that if    then we have to show that   so here zi and yi are random variable…

Q: B) Show that coth-x = In ()

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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: Find numbers m and M Such that m<f'(1)< M figure in (1.4,1.3) l1,2 (1.6, 1,4) +

A: Given: The graph of f as  To find: The numbers m and M such that m&lt;f'1&lt;M

Q: a) Find the values of A and B if - {(x² + Ax + B)e*} = x²e* dx Hence, evaluate S, x²e*dx

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Q: 7π 4 decimals to at least one decimal place. Convert the point (r, 0, z) (x, y, z): = = 6, " to…

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Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

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

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

Q: 1) lag is equal to logizs b)3, c) 3x .d) none of them

A: Solution: log5xlog125x=log5xlog53x we know, logbna=1nlogba hence  log53x=13log5x hence…

Q: and xe"y %3D For ay

A: To find out partial derivatives.

Q: 6.3.6 For each real number x, let Ay = {3, –2} U {y E R : y > x}. Find U Ax and N Ax. xER xER

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Q: Fint the ralue value of the following term 2. 5. 2.

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Q: EXERCISE 5.7.1. Let S := {2": ne Z). Then Acc(S) = □0. {2": ne Z, n<0}. {0}. {0, +00}.

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Q: Find the value of y, given the value of x. 11 a) Cari nilai dy dengan nilai x yang diberikan. de de…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 14 Které číslo se ukrývá v obálce? a) M. (5 + 1) = 36 %3D b) 8. (5 + = 56 c) 4. X+7) = 40 %3D d) 7.…

A: a)    __·5+1=36__·5+1=36__·6=36__=366__=6∴ 6·5+1=36

Q: B=(2,).Then 2 E3 %3D

A: Some definitions: Interval:  Let S⊂ℝ, then we say S is an interval if c,d∈S such that c≠d. Then, ∀…

Q: Y D Prox

A: Product of two sets

Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

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Q: Fad the inverse f AB f 4. 5. and -1 AU

A: Given that , A-1=5-11-5 and B-1=-3-31-1 find inverse of AB.

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

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

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

Q: 8 = 1, EN 7 **** 1'2' M 1" nnn € N

A: