Let A = {x C {0, {0}} | x # 0} How many elements does A have? 1 2 4 3.

Q: (55) Let X = P(1) and E(3x) = E(2– 6x) find 2.

A: It is given that, X~P(λ) Then, E(X)=λ

Q: Let X P(2) and E(x) = E(5 - 5x) find 2. %3D

A: When a random variable follows Poisson distribution then mean and variance of X are same as…

Q: (a) For all a, b e Z prove that a³b² – ab* is even.

A: Properties of algebra Addition of two odd number is even  Addition of two even number is even…

Q: Show that if a f b, then a +b ab ... 1 a +b ab ... 1 a +b an+1 - 62+1 ... a - b ... ... ... ... ...…

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Q: The number of the element(s) of order 2 in Z2 O D6 12 1 11 7 15 24 None of them

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Q: Determine a and b such that p(x) = x2 + ax + b satisfies p(1) = 0 and p ,(1) = 4.

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Q: (b) Determine the value of k for which p(x) = k (0.01)*, x=1, 2, 3, ... x-1

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Q: Find the value of k such that A is singular 1 0 5 4 -1 0 L6 5 k k=

A: given isA=1054-1065kmatrix A is singular if |A|=01054-1065k=01(-k-0)-(4k-0)+5(20+6)=0

Q: Find all values of k such that f (x) is divisible by the given linear polynomial .

A: Given polynomial is fx=k2x3-4kx+3. To find all values of k such fx is divisible by x-1. Solution:…

Q: A factor (x − a)k, k > 1, yields a ________ ________ x = a of ________ k.

A: x=a is a repeated zero of multiplicity k, when we have (x-a)k.

Q: Find a number a + 5 such that S" (1 – æ) dæ = 0

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Q: E(X), E[(X +2)3], and E[6X – 2(X + 2)). -

A: Expectation is basically an average . It gives an value on the long run of a stochastic process .

Q: 12. Find all values of t for which - 1 -2 1+2 0 0 -1 = 0. 0 1+1

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Q: Prove the statement below. Let A = {x | x = 4k for some k E Z} Let B = {x | a = 2k for some k E Z}…

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Q: Let X = P(A) and E(3x) = E(2-6x) find A.

A: Solution: 46. From the given information, X follows Poisson distribution with parameter λ.

Q: The generating function of a_{n+1}=8a_{n}+4n*, where a,=3 is a. Σ2x)^k+Σ (4x) ^{k Ο b. Σ( 2x) ^{k}+…

A: To find the generating function of an+1=8an+4n+1 First multiplying the relation by xn and taking…

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: 2. T = {m EZ| m 1+ (-1)^i, for some integer i} *

A: Given T=m∈ℤ|m=1+-1i for some integer i

Q: Let h(x) = 4x + 5, k(x) = 3- 2x, then the value of h(3) + k(4) is %3D O12 51 48 O None of these

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Q: Find all values of x for which rank(A) = 2. 1 2 0 5 A = -2 -2 x -1 3 8 -2 24 x =

A: Given: The given matrix is, A=1205-2-2x-138-224 Also given that rank(A)=2 The objective is to find…

Q: Let X have the pmf p(x) = (12 )x, x = 1, 2, 3, . . ., zero elsewhere. Find thepmf of Y = X3.

A: We will use the following :  Discrete random variable X is variable which has finite or countable…

Q: 2 guestion 12 If for all real values of x, (x + c)(x + 4) = x´ + 8x + 4c, then c = ? eport Issue…

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Q: xdx Evaluate: 5+x2 A In(x²+5)+C x²+5 (B) In +C 2 None of the given choices D 21n(x²+5) +C E…

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Q: Determine all values of x so that det(A) = 0, where

A: Determine all values of x so that det(A) = 0.

Q: Find the coefficient of a' in the expansion of: (a) (1 – x)-4x (c) x²(1+ x²)*(1– x)-3 (b) (1 – x)-2x…

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Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

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Q: (5) If f(x) =........, then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x² +…

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Q: Let h(x) = -3) Then, h(x) has a zero on (0, o). —1) (ӕ+2)(2+3а) O True False

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Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: formResponse [1 Let A = 0 Lo 3 2 31 1 1. Which of the following is true about A-1? 4]

A: If the matrix A = a11a12a13a21a22a23a31a32a33 , then det(A)= a11…

Q: What is z if x = 100, µ= 105, ở = 10, and n = 25? Н 1.5 F -2.5 H G -1.5 J 2.5

A: Solve by formula

Q: the value(s) of c such that 3c2n n=0

A: The given question is taken from the sequence and series in which we have to find the value of the c…

Q: Let x² – x – 2 h(x) = x² + 4x Find all the values of x that are NOT in the domain of h.

A: For a rational function, denominator should not be 0.

Q: Given z(x) = -x2 Find the following: z(3) z(-2) z(0)

A: z(3)=-(3)2       = -9

Q: Let S be the set of integer solutions to the equation x1 +x2+x3+x4 = 30, where x; > 0 for i = 1,2,…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Solution:-

Q: Let f(x)=X13, ga)= 2R-1, and h(x) : 2x* + 2n-12. Wiite a formula and Simplify for: (fh)(x)= ell

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Q: If X-P(A) such that, P(X = 1) = P(X = 2) then find A. %3D %D O None O A=V2 O A=V3 O A = 2

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Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

A: Introduction: For a function f(x,y), the degree of homogeneity is an integer n such that,…

Q: 3. Suppose that the pmf of X is x-1 1. p(x) ,t = 1,2, 3, . 3 3 Find the mgf of X.

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Q: Find all values of x for which rank(A) = 2. -1 2 0 5 A = 2 -2 x -3 -1 4 6 12 x =

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Q: Let A = {x x = 12k for some k E Z} Let B = { x | x = 4k for some k EZ} Prove that A CB.

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Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

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Q: Let X = P(2) and E(3x)= E(2-6x) find 2.

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Q: In D, find all elements X such that a. X³ = V; b. X³ = R90' c. X³ = R₁; d. X² = Ro e. X²2 = H.

A: We have to find X in all parts

Q: (a) Find the extreme values on [–1,4] of p (x) re-z²/8. = xe

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (5) If f(x) =........, then f(x) is reducible in Z5 [x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

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Q: Find all values of k such that f (x) is divisible by the given linear polynomial .

A: Given: fx=kx3+x2+k2x+3k2+11, gx=x+2 We know that if given fx is divisible by gx then x=-2 will be a…

Q: 8. x* + 2x² + 4 is reducible over Q a) True b) False O a) True O b) False

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Q: {1 + x + x, x + x², for P2. Let >(x) = p(x)]B = 1 + 3x + 2x2. The

A: Here we have, B=1+x+x2, x+x2, x2  for P2. Let p(x)=1+3x+2x2 We have to find, p(x)B=?