Suppose X ∼ Binom(n, p). Show that E[X] = np.

Q: I got 0 but idk if thats correct please show all work

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Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

Q: If X ~ N(5,2). Calculate P(X<6) [Draw a figure]

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Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

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Q: Suppose that X ~ B(30, 0.67). Find q. Submit Question

A: In question, Given that, X~B(30, 0.67). Then we'll find value of q? The solution below,

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

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

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

Q: Hypothesis Testing for Two Proportions Preform a hypothesis test on a separate sheet of paper Nathan…

A: According to our guidelines, we have to sove only first problem.

Q: There are 5 types to solve linear diff. eq. of first order * True False

A: Given that , Linear differential equation-A linear differential equation is defined by the linear…

Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

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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)&gt;2sts-t

Q: Use proof by contradiction to prove that if x + y &gt; 2, then x &gt; 1or y &gt; 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: Linerije he lien apantion: 1. yeation; nen- x* xy+ 3y sie the ryin *T/ テ

A: Solution: We have to linearize the equation z=x2+xy+3y2 within the region 2≤x≤3,  11≤y≤12 Let us…

Q: is o(x). Hint: Use ling divisim

A: Let consider  fx=x4+x2+1x3+1 To show that f(x) is O(x).

Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Suppose X~N(19, 2.5).  Find P(X = 17)

A: Given X~N(19, 2.5)

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

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: Is Q closed over multiplication? (Y/N)

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Q: 5. Evaluate J2xdx, a, x' +c b, x+c C. 2x+c

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Q: Linearize x³ + ln x about x=3

A: Let f(x)=x3+ln x about x=3 f'(x)=3x2+1x Recall: Linearization  L(x)=f(a)+f'(a)(x-a)  we have a=3

Q: Show that is isomorphic to Z2.

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Q: Let G = (a, b | a² = b² = (ab)?). a. Express b²abab³ in the form b'a'. b. Express b'abab³a in the…

A: Given: The expression is G=a,b|a2=b2=(ab)2. To Express: (a) The expression b2abab3 in the form of…

Q: 1. [-(p A -q)] V -r

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Q: Provide an interpretation which is true and one that is false. (∃ x)(P(x,b))

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

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Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: Let X N(10, 23). Then P( X< 10) = %3D

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Q: Let N={1,2,3,4,...}. Let P(x,y) be the predicate that x is less than or equal to y^2

A: (d) S = {1, 2, 3, 4, 5, 6, 7, 8, 9} (e) T = {3,4,5,6,......} (f) R = {} (empty set)Explanation:(d)…

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: Let X N(10, 23). Then P( X< 10) =

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Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: 4. Show that it has a real value!

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Q: (9) Let P, Q, R be (a) (¬P VQ) (b) (P mathematical statements. Negate the following statements.…

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