Q Let (X, B(R), µ) be a Borel measure space. Suppose that{An = [2n-1 3n+1]]∞ Then µ(U("1, 4n-1]) equals be a family of elements of B(R). n n lSn=1 n=1 a.0 b.1 с. 3 d.4

Q: 1 nt) Consider the function f(x) = 6x2 +3 is concave up for x E isqrt6/6, infinity is concave down…

A: The concave up and down nature of the function is determined by the sign of the second derivative of…

Q: Oz Aradom Variable(x) has the following cof FX(X) = (x³ + x) al find the pdf of X find Pro <xcot)…

A: Given that: The cdf of random variable X is given as: FxX=12X3+X      where 0≤X≤1

Q: The constant k which satisfies P(k <T < to.2) = 0.3 is: %3D А. -to.2 В. to.1 С. -to.1 D. None of the…

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

Q: How many real valued solutions over (-1,1) to the following ODE?

A: given odinary differential equation  y'=x1-y'+ylnlny'+eπxy claim-  to check how many solution does…

Q: Suppose X~N(197,6), and Z~N(0,1). Then x = 189, is equivalent to z = ______

A: Given Information: X~N(197,6) So, mean μ=197 Standard deviation σ=6 X = 189.   Z-score or…

Q: Suppose X~N(180,15), and Z~N(0,1). Then x = 185, is equivalent to z = ______. (Round your answer to…

A: Given that, x~N(180,15)  Mean = 180  standard deviation = 15  We know that z-score is given by,…

Q: Show that 8(x) E Q, which will h.q.h-¹ EhQh-¹ is also an element of Q. Hence 8(x) E Q so that x E P.…

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Q: Consider the function f(x) = x° on the interval 0, 1]. Compute 1 3 x°dx using the following steps.…

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Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

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Q: + 2x Compute dæ. O 3(z+z²) +C 1 1. I미 피 + C 2 O x +2 ln |æ|+C

A: Given: I=∫1+2xx2dx

Q: Əw 1. If w=x" f() show that x ax +y Əw ду = nw where n = integer.

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Q: Let x, y be two positive real numbers such that x?y + 4 = a where a 2 4. What is the minimum value…

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Q: 1. We can generalize our approach to warto for any state function. Consider: f = 3x²³ - 2xy² for X₂…

A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

Q: 6-2 x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y,

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Q: 3. find the Lem and hef of 12,15 andh 2kyapplying the pacene factoce. eatial mothod 2x 2x 3 3 X5 2…

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Q: X=(1,0,– 1, – /2)'. Then,||X||3 = ect one: a. b. 2 C. d. V2+2/2

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Q: 3. Find the sum of all values of k such that 2k k -dx =15. (A) 3 (B) 2 (C) 1 (D) 0 (E) 1/2

A: ∫12kx-kx2dx=15∫12kxdx-∫12kkx2dx=15∫12kxdx-k∫12kx-2dx=15x2212k-kx-2+1-2+112k=15x2212k-kx-1-112k=15x22…

Q: (15.2): Find In(x) – In(x² – 1) +2 In(z +3) 3

A: Find 13ln(x)-lnx2-1+2lnx+3. Logarithmic properties used: alogcb=logcba logca-logcb=logcab…

Q: 26. Let u be the Lebesque measure on B(R). Calculate (i) 4(S), where S {n,nE N} (i) ul13 7 0) uhre O…

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

Q: 4. 9. 99 24 +. 20 10 10. 5. -88 +. -5 -3 11. 6. -20 30 +6 +5 8. 11

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Q: USE THE FOLLOWING INFORMATION FOR QUESTIONS 1.8 AND 1.9 d'y dt? 1.8 The auxiliary equation, roots…

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Q: Q=[X1,2,3,X2- A. length(Q) B. Q(1:4) C. Q(5) ==0 D. max(Q) E. sum(Q) F. Q'

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Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

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Q: If X~ Uniform(b, 1) and o² = 3μz, what is b? (a) -0.82 (b) 12.18 (c) 20.82 (d) 17.00 (e) None of the…

A: To find the value of&amp;nbsp;b, we first need to find expressions for the mean μX​ and…

Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

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Q: d K, d1 + d. +... + K, 2 n K, K, 1 n

A: Let d=d1+d2+....+dn From Cauchy Schwarz inequality , we have- d1k12+d2k22+.....+dnkn2…

Q: Suppose X~N(165,16), and Z~N(0,1). Then x = 173, is equivalent to z = ______. (Round your answer to…

A: Given: X~N(165,16) μ=165σ2=16Thus, σ=σ2=16=4 And X=173

Q: Q6. Let u be the Lebesque measure on B(R). 4n-i n+3 Calculate (i) µ(S), where S = {,ne N} %3D (ii)…

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Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

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Q: Suppose X~N(148,8), and Z~N(0,1). Then x = 143, is equivalent to z = ______. (Round your answer to 2…

A: Given information  X ~N(148,8) Population Mean (µ) = 148 Standard Deviation(σ) = 8 X= 143

Q: We know [n] = {1, 2, - . , n}. Let A = [8], B = {x € A : x > 5}, and C = {x € 1 (D

A: Cartesian Product of two sets: A×B denotes the Cartesian product of two non-empty sets A and B. Also…

Q: Suppose X~N(125,16), and Z~N(0,1). Then x = 141, is equivalent to z = ______. (Round your answer to…

A: For large sample n&gt;30 so, it is a z test. x~N(125,16) =125+16 = 141= x.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.