Theorem 3.1.6 Every non-negative real valued function f that is integrable over the real axis and satisfies iedt anilia bs Š(2) dx = 1 - 00 is the probability density function of some continuous random variable.

Q: Using Part(a) of this problem prove that [*r(e) f(x) dx < [*9(x) a g(x) dx

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Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(A U B)…

A: Let A,B not empty, bounded subsets of R .Prove thatsup(A∪B)=max{sup(A),sup(B)}. Let: ⇒x∈A∪B⇒x∈A or…

Q: 4 is this the SAS or SSS theorem?

A: Given questions is SAS property First , we have to know to SAS or SSS property  SSS (Side-Side-Side)…

Q: Which of the following is the derivative of f (g(h(x)))?

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Q: Let G be a group and a be an element of this group then necessarily: Jal|G| O lal=IG]|

A: Second option is correct.

Q: Show that

A: Our Aim is to Prove that:-111abca2b2c2=a-bb-cc-a   -(i)

Q: Show that y = sin (1/x) has no limit as x approaches zero from either side

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Q: Prove Theorem

A: (a)   Let A=a11a12...a1na21a22...a2n⋮⋮⋱⋮am1am2...amn…

Q: eimil 2.5 THEOREM Suppose f : D R and g : D→ R, xo is an accumulation point of D, and f and g have…

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Q: Consider the tennis balls shown in the accompanying figure. Assume that one tennis ball is randomly…

A: Total number of balls = 6  Total number of orange balls = 3 odd number balls = { 1 , 3 , 5 }

Q: Prove property 4

A: Let ϕ is an isomorphism from a group G onto a group G. We have to prove ϕK=ϕk|k∈K is a subgroup of…

Q: Prove VnEN, + + + 1 2 3 1 + ≥1+ 2n 1 2n n 2

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Q: W Let z = x₁ + iy₁ and w = x2 + iy2. Prove = e²-w ew

A: ex × ey  = ex+y  e-x = 1/ex

Q: (8D°- 4D?- 2D +1)y-o Answer: y= (Catc2x) exp (x) + Cs exp (-*)

A: The given differential equation is 8D3-4D2-2D+1y=0 Solution can be calculated by using its auxiliary…

Q: [Problem 1] Prove the following statements formally. a) Let f(n) b) Let f(n) = = log2 (n) and g(n) =…

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Q: Prove Unjustified Claims Justified Claims O KAOBE4COA O is the center of O01 f KAOBEKCOA AB is…

A: The objective of the question is equivalent of the angle.

Q: survival analysis and forecasting. Since half logistic distribution is formed by using absolute…

A: Solution: It is needed to prove that half logistic distribution with only positive value and a zero…

Q: 1.2. [2, 5]U[3, 7]=[2, 7]. EX LET x€[2,5]U[3,7]

A: To complete the proof, one must find that

Q: Consider the function, f(x) = x³ + x² – 9x – 9. (a) Graph the function. (b) What are the x- and…

A: Given,  f(x)=x3+x2-9x-9.

Q: Theorem 31. Let F be an ordered field with ordered subfield Q. Then F is Archimedean if and only if…

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Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: Suppose V₁,..., Vm € V. Prove that {v₁, ..., vm}¹ = (span(v₁, ..., Vm))¹.

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Q: What is the area of this figure? 8 yd 2 yd 3 yd 6 yd 2 yd 3 yd 4 yd 5 yd 9 yd Write your answer…

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Q: - Use the division algorithm to find the quotient q and the remainder r when dividing f(x)=x³+x² + 4…

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Q: y = (cos(3x))*

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Q: Theorem 11. Let A E Mn be positive semidefinite . Then A has a real root. Moreover ,the square root…

A: Given: To explain the given statement as follows,

Q: Every solution of an Euler equation to the right of a regular singular point, xo, has a mirror image…

A: Given: Every solution of an Euler equation to the right of a regular singular point x0 has a mirror…

Q: Prove the theore

A: The theorem states that for a nonempty subset E of R, if a is an element of E and f is a function…

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: 2 C, e-kt Show that the equation dy + 2k - possesses solutions of the form 00 cos (C, x+ E,) cos…

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Q: 14) Suppose that an honest coin is tossed ten times. What is the probability that it will come up…

A: Let p be the probability of getting head  n be the number of coin tossed  X be the number of getting…

Q: If G is a graph, then the sum of its vertex degrees is nonnegative and even.

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Q: Question 3 Let Ank be the number of partitions P of the set {1,2,..n + 1} such that {k +1} € P but…

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Q: Prove inf { t IneN}=0 4n : nE IN Prove sup

A: We have to prove that the  Infimum { 1/n | n in N } = 0.

Q: Find fy (x, y) for f(x, y) = . eły

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Q: Prove the property.

A: To prove,

Q: (j) 5″ n! π

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Q: Use E-N verification to prove that n² n²+n las n→ ∞o.

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Q: Exercise 36. Prove the above theorem. Hint: some pieces have been done in earlier theorems and…

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