ssume X ∼ Poisson(r), where r > 0. Prove that E(X) = r.

Q: Evaluate: a In(x + y) e-y. dy dx

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Q: (13) Prove by induction that for each whole number n, 1. You may use the fact that for each whole…

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Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: 1 Prove that 3 dx s VI VI

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: 2 1-X ie 2=tny then prove that da

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Q: y" +/ sin a = 5 + e %3D

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Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Use mathematical induction to prove that cos(x+n) = (-1)" cosx where n≥le J*.

A: Mathematical induction is defined as a mathematical technique that is used for the expression,…

Q: Use Cauchy to integrate the following T ez - e-z 24 dz

A: The integral  is :The main to evaluate the integral using the Cauchy formula

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: Find the first 3 Zerms o Sinx et a =?

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Q: Show that sin(x)  can be approximated by x-x3/6  within 0.01 on the interval [-1,1].

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Q: 77. Find - Ans. (sin t – cos t + e-t) (8+ 1)(82 + 1) |

A: Topic:- inverse Laplace transform

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: Prove the following identity: (x + y)2- (x-y)? = 4xy %3D

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Q: cos ax -dx = te' 2 х* +1 ле",а 20.

A: In this context, prove ∫-∞∞cos axx2+1dx=πe-a,a≥0. Consider, ∫cfzdz=∫-∞∞cos…

Q: ) Prove that sac"()/T sec

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Q: The area of the segment of a unit circle, A is A = ²(0 - sine) where 0 is in radians Dotorming A if…

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Q: P2: |(e* sin x + x In x) dx

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Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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Q: a) Evaluate r(금). r(0)

A: According to our company policy, we are supposed to answer the only first question. For the rest…