Then P (X + Y ≤ 1|x ≤) is:

Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

A:

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

A:

Q: (b) Let x € R. Prove that if x² – 2x − 3 ≥ 0, then x² + 1 > 0. -

A:

Q: Section I 3. Suppose that X is a discrete random variable with pmf |4- r|+ 4 f(z) for =-6,-3,0,3,6,…

A: Solution

Q: x, y, z)=x²√√x - y² - z²

A:

Q: Find + ][a³dA where R = {(x, y) | 25x² +9y² ≤ 225} R

A: The given region is ellepse and we have to convert it into circle. Then we apply the integration.

Q: 7 (:) Prove that f(x) : is convex.

A: Given the function f:ℝ→ℝ2 by, f(x)=xs Note that the domain of the function f(x) is convex.

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: Suppose UCC is a domain, f, g = O(U). If |ƒ(z)|2 + |g(z)|² = 1 for all ZEU, show that ƒ and g are…

A: The solution to the problem is in the segment below.Explanation:To show that f(z) and g(z) are…

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: (а b)с + (а - с)b + (с b)a 3 ve that v belongs to B.

A:

Q: Prove that for any x, y ≥ 0, we have √x - √y ≤ √√x - y). (Hint. Consider the cases x≤y and y ≤ x…

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Q: Let x, y ∈ R such that x 0.001. Prove that |x · y| = |x| · |y|

A: Given: x, y∈ℝ, x<-0.001 and y>0.001   To prove: x·y=x·y

Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

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Q: X x² + 1 Let f: RR be defined by f(x) = f is a Borel function. O f is not a measurable function. a.…

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Q: Find ||F||. F(x, y, z) = i + j + k

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Q: Prove that P[X |Y ] = (P[Y | X] · P[X] ) / P[Y]

A: From the definition of conditional probability, for two events X when Y is given PX|Y=PX∩YPY

Q: Let X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently. 1.…

A: X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently.

Q: Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

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Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

A:

Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

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Q: (B) Prove that (Q,|·|) is not complete.

A: A metric space (X,d) is said to be complete iff every Cauchy sequence in X converges to a point in…

Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

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Q: 5. Prove that if ƒ : [-1, 1] → R is measurable, then |f| is also measurable.

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Q: h2 |w(x) = Let h = x1 – xo, and w(x) = (x – x1)(x – xo). Proof that max %D 4

A: Let w(x)=x-x1x-x0 where h=x1-x0Prove that wx=h24.

Q: 18. Let A = {1,2, 3}, B = f: A → B, and g : B → C, such that {W, Y, Z}, C = {7, V2, V5}. Find…

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Q: Let A = Z and B = Z. Suppose f: A ∈ B is defined by the rule f(a) = a3 + a + 1. Determine f(−1) and…

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Q: 2b. In R show that : || x - y || || x + y || ≤ 11x11 ² + 11y11²2² -(1

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Q: Consider sets A and B with |A| = 12 and |B|| 8. How many functions f : A → B are surjective?

A: We will find out the required value.

Q: or the given function f(x) = [3x + 5], compute f ({2}).

A:

Q: If |Z| ≤ 1 and w) ≤ 1, then show that |zw|2s (1z|-|w|)² + (arg z - arg w)²2.

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Q: If a < c < b and f(c) is the greatest value on the interval (a, b), then f(c) is a ....

A: