Show that E[X]= a +V and o = b 4 4 -

Q: 0.9pt # BIUS A A o X2 x E Times New Romana 14px 56x3/14 12 13) 14) 90 10 14 10 56 40 36 3. 14 14 126…

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Q: Find [4x³ (In x)² dx. O A. 1.4 X x In²x + In x + O B. x² ln² x - ln x + O C. x ln x O D. x ln x X 2…

A: Note : according to our gauideline, i can solve oy first so please reroute the remaining question.…

Q: is given by Oxy = E(XY) HxHy.

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

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Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X & Y are independent then we say that…

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

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Q: Evaluate the integral. 2+e-2x dx e3x 10 +C O -2e-5x(5e3x + 1) + C e Sx(10e2x + 3) + c 15 1 e 3* 2e2x…

A: The given integral is ∫2+e-2xe3xdx. Evaluate as follows.…

Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.

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Q: 2 Calculate e(0) and e(0) for 1.98z E(z) = (z? – 0.9z + 0.9)(z - 0.1)

A: Ez=1.98 zz2-0.9z+0.9z-0.1Now put the value z=0E0=1.9×00-0+0.90-0.1=0Becouse 0x,x≠0⇒0Now E(z)=1.98…

Q: Find a general formula for dr ax + b dx" cx +d

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Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: Let Pr[E]=0.7, Pr[F]= 0.3, and Pr[E^F]=0.2 Find Pr[EUF] O 0.5 O 0.4 0.6 0.8 0.2 O 0.1

A: Let A and B be any two events, The formula of P(A union B) is,

Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: 6) If G(x) = In(t) dt then G'(x) = 2x*e=*. a) True b) False

A: We need to determine whether the given statement is true or false. Statement given is- If…

Q: Evaluate the following integral e-24 8(t – 1)dt A) e-2 B) e² C) e-1 D) E) 0 e

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Q: Find the general solution to the Bernoulli-type ODE x²y' + 2xy = y°, for x > 0.

A: Bernoulli's equation is a special type of first-order linear ordinary differential equation. When…

Q: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: Work out the following | (2x + 1)e² -z da =

A: we use substitution method to solve this integration

Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: Evaluate e dt 0.2

A: We have to use standard gamma integration here.

Q: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

A: Here we have to use fundamental theorem of calculus to find the exact value of  ∫05(x3-9x)dx…

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: Evaluate the integral. 8+e-5x dx e6x 1 44 -5x +6 + C 30 O -8e-l1x(11e6x + 1) + C O .tel1x(88e5x + 6)…

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Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

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Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: Suppose E(X) = 4 and E[X(X – 1)] = 25.5. (a) What is E(x2)? [Hint: First verify that E[X(X – 1)] =…

A: Given: EX=4EXX-1=25.5 So, a) EX2-X=25.5EX2-EX=25.5EX2=25.5+4=29.5

Q: solve for x if CDy=4(x-E)

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Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Evaluate the given function (e²x – 1)dx = (e2* + 3)(e" – yº)dy is equal to. 3y°+1 = x + 3e –…

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Q: e 2x Evaluate the integral of e* +1 xp-

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Q: • In z Find F" (2) if F(x) et dt a² _4 O A. 1 O B. 0 Ос. -2 O D. -4 O E. –3

A: Given:         Fx=∫x2-4ln xet dt                 =etx2-4ln x                 =eln x-ex2-4…

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: prove that d/dx xn=nxn-1

A: To proveddxxn=nxn-1

Q: Given f(x)=e*, g(x)=5* , and h(x) =g(x)/f{x), find h"(x). A) 5*e*(In5+1)² B) 5*e*(In 5–1)² C)…

A: Consider the functions  f(x)=exg(x)=5x and  h(x)=g(x)f(x)=5xexh(x)=e-x5x

Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…

Q: The function f(x) = (6x+5)e^4x has one critical number. X= ?

A: Proceed as shown below...