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

Q: 3 -7 [3] 7 -5 Let E= -2E= 0 Find -2E. 00 8 [000) 000 1000 [00] Undefined

A:

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

A:

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

A:

Q: 7.5.7. (a) Let an (b) = 0 for n ≤ 100 and an {bb 1 for all n}. == Let a, = { bb, = 1 for n> 100.…

A:

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

A:

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

A:

Q: E(X), E[(X +2)3], and E[6X – 2(X + 2)). -

A: Expectation is basically an average . It gives an value on the long run of a stochastic process .

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

A:

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: 1. Thermal Inversion When there is a thermal inversion layer over a city (as happens often in Los…

A: rt=2t  &  Ar=πr2 a). Art=A2t=π2t2=4πt2 The area of the circle after t hours is 4πt2.

Q: Let à = − 3ỉ − 2j + 2k. Find ||ā||.

A: Find the square root of the sum of the squares of the coefficients of each unit vector.

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…

A:

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…

A:

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

A:

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: 11.1.5 Show that (a) cosx = Jo(x) +2(-1)" J2n (x), n=1 (b) sinx =2)(-1)" J2n+1(x). n=0

A:

Q: Liouville function X(n) is given by formula

A:

Q: e value of t

A:

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

A:

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

A:

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

A:

Q: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

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

A:

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…

A:

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

A:

Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

A: In this question, we use the definition of Riemann integral to check the function H(x) is Riemann…

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

A:

Q: 6. Suppose an 2 0, and a, diverges. Show that C dn diverges. an+1

A: For the solution follow the next step.

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: п(3п - 1) (b) (3i – 2) = (for n > 1). - i=1 (0) II (- n+1 (for n 2 2). i2 2n i=2

A:

Q: 1. Determine a condition on |x − 1] that will assure that: - (a) |x² - 1|</ (b) |x² - 1|<1/10¯³, (c)…

A: 1) (a) Given inequality is So either  .  because, So combining we get

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.

A:

Q: Convolution. Find the convolution of (a) Πα * Πα. (b) f(x) * ƒ(x), where ƒ(x) = e¯\ª\, -∞< ï<∞.

A: As per the question we are given two functions as: Πa(x) : the rectangular pulse function with…

Q: 4 5) If L f(t) es find L f(4t) Ans. e s

A: Laplace transferom of change of scale property

Q: 18.1.20. Let R = Z[√³]. Find 14 different units and 10 different irreducible ele- ments of R. How is…

A: To find the integer solutions to ( x^2 - 3y^2 = 1 ), we essentially need to find the units of ( R ).…