1. We have -o (") = 2". 2. For 0

Q: 1. 3. Determine [[e=²*² +25-+²] kt [[e+cos (√2+)] [[ext_H(t-a)]

A: Given : 1. Le-kt+2π-t42. Le-tcos2t3. Le-2tHt-a

Q: 1 s(s+1) 6) L'

A: Given: L-11ss+13

Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y = min(X1,..., Xn) is also exponential…

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Q: Find In (6) In (4) 2 - 3y dydx - x - 3y e

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Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: 7. Find A. 6 C. 2 fre f(x) dx, given [*[³f(x) + [3f(x) + 4] dx = 18 B. 10 D. 14 3

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Q: 17. Determine k so that d(x) is continuous -x-k, ifx-1 [2x+ 2k, if x = -1 d(x) =

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Q: 5.2.3. Let f be the constant function f(x) := 1, and let g(x) zfotion g(x) := e2nia. Then Show (f,…

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Q: Let f(x) = cos(x²). Then f(20)(0) = Select one: a. Non of them b. 1 (10)! (20)! C. (20)! (10)!

A: Solve the following

Q: 12.1.1 From the product of the generating functions g(x, t) g(x, -t) show that 1 = [Jo(x)]²+…

A: Starting with the generating function for the Bessel functions, we can use the generating functions…

Q: We know that (+)' = Find A A = x (Ax+B) (x+1)²

A:

Q: 1.7. (-) The statement below is not always true for x, y e R. Give an example where it is false, and…

A: given that if x and y are nonzero real numbers and x>y then (-1x)>(-1y) in the first case we…

Q: 5. Given n constants ki (with i = 1, 2, ..., n) and n functions f(x), deduce from Rules Iv and V…

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Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: 7. The famous Rodrigues formula states that H, (x) = (-1)"e*² (4)" functions for positive integers…

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Q: 2.25 † Let I" -a" if x + a, f(x) = I-a if x = a, where n e N. Find the value of e that makes f E…

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Q: 5. Let fe L(X) such that ker() = ker(f2). Show that X = ker(/) (X)

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Q: 10 Suppose that Pr[A|B] = , Pr[B|A] = , and Pr[A'] = Find Pr[A n B']. 21 15 11

A: From Pr[A'] we find Pr[A]

Q: e value of t

A:

Q: 4.1.1. Determine a condition on |x-1| that will assure that:

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Q: Only one of the following statements is (always) correct. A) If any vertical line intersects the…

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Q: 11.2.7 Prove that d P(1) = P(x) = n(n+1). dx

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Q: 4. (a) Two fun results about natural logs: i. Choose k 2 e*. Then show that (In k)Ink > k². ii. Show…

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Q: 13. Prove E-1(4i – 3) = n(2n – 1) for natural numbers n > 1 %3D

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Q: 1. Which of the following relations is FALSE. n+m A) (ab)" =a"b" B) C) (a")" 2. The equation of the…

A: To identify the false relation from give question.

Q: 1.8.6. Let the pmf p(r) be positive at r = -1,0, 1 and zero elsewhere. %3D (a) If p(0) = 1, find…

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Q: o.10. Prove that (a) J,"(x) = ¿[J,(x) – 2J,(x) + J, + glw). n n-2 n' n+2

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Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: 1.2. Example. Find the order of the following functions (i) f(z) = ao + a¡z + a2z +...+ anz", an +0…

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Q: e examples. Let Pr = 1/2, 4x = Do = 1. For large x, qa (1 – cx-a)/2, but the ex keeps the…

A: *Answer:

Q: 1. Show that b, = (n!)'/n > 20.

A: Consider n!1n=an1n.

Q: 3. Suppose that the pmf of X is x-1 1. p(x) ,t = 1,2, 3, . 3 3 Find the mgf of X.

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Q: S={Awirn ertes (o.0) (1,!) (lor) 9 = 1oX

A: