Property 3. If X is a random variable and ´a' is constant, then E [a ¥ (X)] = a E [Y (X)] E [Y (X) + a} = E [¥ (X)] + a, where Y(X), a function of X, is a r.v. and all the expectaiions exist. (i) %3D (ii)

Q: a a +1 2² (² + ¹ + x² = 1 [(¹-x)² + (1 + x)² ] F1 2 2 2

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Q: X* +39

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Q: Prove that AAB = (AU B) - (An B),

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Q: Prove. Z40 (Rez) ² +Z1 ? 0

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Q: 1+ sin 0 csc0+1 1-sin 0 csc0–1 II

A: We have to prove the identity.

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A: The answer provided below has been developed in a clear step by step manner.

Q: Construct a proof that ZEIF = ZGIH. н

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Q: Recall the property that (a, b) = 1 if and only if ax + by = 1 for some integer x, y. Use this…

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Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Show all formula, substitution and calculations. Round off to 2 decimals. In how many ways can…

A: The collection of items or elements arranged in a different way with ordering is called Permutations…

Q: State the Fermet's Last Theorem. Who was French women mathematican who mede significant 19th century…

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Q: Show that if a and b are real numbers and a!=0 then there is unique number r such that ar+b=0

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: Z

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Q: Show that (A\B)\CC A\C.

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Q: prove that div A マ - Kr

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Q: Suppose A=| use Diagonalization to compute A" 10

A: In the given question we have to find the 10th power of the matrix A s.t A=10-12. Concept: If a…

Q: The birth weights of newborn elephants are Normally distributed with a mean of 160 pounds and a…

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Q: Indicate that  R and R2 may be covered by countably many open balls.

A: To show that ℝ and ℝ2 covered by countably many open balls.

Q: dz

A: Wallis FromulaFor  positive integer n∫0π2sinn x dx=∫0π2cosn x dx       If n is even   1.3.5. ...…

Q: Prove that (An (BUC)) = AU BUC.

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Q: Verify that there is no magic square of order 2.

A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: Let A = {5, 10, 15, 20, 25) and B = {3, 6, 9, 12) (a) Find A - B (b) Find B A (c) Based on your…

A: we know that A-B=A\B=all those element of A which are not in B.Simialrly, B-A=B\A=all those element…

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: Prove bey wnduc hiou that for n22.

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Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: what is the characteristic of Z6xZ9

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Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: A2

A: Consider the matrix A is, A=0100 Apply the condition, A2 = O. 0100·0100=0000 The matrix A is…

Q: is it proveable with only the theorem given?

A: Is it provable with only the theorem given?The notations and symbols in the given theorem are used…

Q: 1. Solve the equations below. Show your work. a.) x2 – 14x + 45 = 0 b.) 3x2 – 2x - 5 = 0

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: 4. Ax (1-22, 1+22) where A - Z 5. Ax(0, 32, 62) where A - Z 6. A, [5, 10- +] where A = Z' 7. Ax (5+,…

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Q: 1) D Prove that 224 O 210

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Q: List the elements of U(18).

A: The elements in  which are relatively prime to are the elements of ..Two integers  and  are called…