The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.

Q: Question: 1. If A = =1²₁ NOTE: 0 51 1951 then find the factorization of A.

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Q: Using the Maclaurin series e² -> [²4-2 -² dt 71-0 3 find the general term of the Maclaurin series of…

A: Given: The Maclaurin series is given by ex=∑n=0∞xnn!. To Find: We have to find the general term of…

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Q: 15. Find the equation of the tangent line at the point (1,0) if r² sin y = ry² + 1.

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Q: 2. Solve dy dx -5x + sin 3x + 2x; y(0) = 2

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Q: Below is a Study which Aims to Determine if HAVING A JOWA AFFECTS THE GRADE OF TIP STUDENTS STUDENT…

A: STUDENT GRADE BEFORE GRADE AFTER 1 85 87 2 50 83 3 65 48 4 85 46 5 45 74 6 36 94 7 35…

Q: = Determine if the vector field F(x, y) function f(x, y) with Vf = F. (yery)i + (rey) j is a…

A: To prove conservative:

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A: Given recurrence relation  an=-2an-1+8an-2

Q: 11. Find all the zeros of f(x)=x²-x²-4x² +8x²-32r+48 using synthetic division. Write fix) in…

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Q: What are the last two digits of P? 1000 P = II [5 + (−1)”] n=1

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Q: 1. Prove that the linear map d : ax (C¹([a, b]), Il-ll) → (C([a, b]), ||-||) dx is not continuous.

A: Since you have posted multiple questions, so as per the guidelines I am supposed to solve only first…

Q: What are the integer solutions to the following system of equations? √x + y = 7 x + √√y = 11

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Q: 4) Find the area of region that is inside the cardioid r = a(1+sin 0), outside the circle r = a sin…

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Q: the Laplace transform of the following function. (Enter your answer in terms of s.) g(t) = 4t² -…

A: The given function is gt=4t2-3e2t. The Laplace transform of the function is obtained by, Linear…

Q: S4.6 Area Inside a Polar Curve Find the area of the interior of the cardioid: r = 3 + 3 cos (0) Area…

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Q: 5x+(1)/(2)-(6)/(x)explain how you get each term of the quotient

A: The given equation is 5x + 12-6x. So, We need to explain how to get each term of the quotient.

Q: Use polynomial fitting to find the formula for the nth term of the sequence (an)n>1 which starts,…

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Q: Find a parametric representation for the surface. the part of the ellipsoid x² + 7y² + 5z² = 1 that…

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Q: Q1. Show that the function y(x) = xet is the solution of the Volterra integral equation y(x) = e³…

A: Given function: yx=xet To Show: The given function is the solution of the Volterra integral equation…

Q: Theorem: If B Is a base for topology J on set X and B₁ is a family of subsets of X such that BB₁J…

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Q: Let P be the tangent plane to the graph of g (x, y) = 20 10x² - 20y² at the point (4, 2, -220). Letf…

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Q: Question 8: Consider the differential equation: dy : = x + y² with y(0) = 1 dx Use Euler's numerical…

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Q: Recall that M₂ (R) denotes the vector space of all 2 × 2 matrices with real entries, i.e. M₂(R)-(())…

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Q: 9. The differential equation has a power series solution A) -3 B) -1 6 for some constant real…

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Q: Solve 6 []-[20 -20 Q- 131: = Y x(0) = 4, y(0) = −18 -181

A: Finding eigenvalues of Coefficients matrix:

Q: Establish the (Green's function) identity, COS 2 cos (nux) cos (nity) n²π² n=1 = 1¸ x² −x+y²…

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Q: 6. Solve the following equations. State exact answers. a. log₂ (x) + log₂ (x + 2) = 3 14x² = 2x+6…

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Q: ]Find the directional derivative of the function f(x, y) = x sin(x y) at the point (1, 7/3) in the…

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Q: Let V be a vector space over R. Suppose {v, w, ż} is a basis for V. Prove that {+w, - w, ż} is also…

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Q: of cookies. To thank your math professor for doing such an amazing job all semester, you decide to…

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Q: The differential equation of a system is given as y" +5y' +6y=e-t, output y are functions of time t.…

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Q: A homogeneous rubber string of length 5 has its initial points displaced by x/2 and then oscillates…

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Q: Diagonalize the matrix, if possible. Enter "DNE" (without quotes) in each of the answerboxes if the…

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Q: Let V be a 5 dimensional subspace over R. Let U and W be subspaces such that dim(U)= dim(W) = 3.…

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Q: 10. Given f(x) = a. b. C. d. 4(x-2)(x-5) 3(x-2)(x-6)' determine: the x-intercept(s), if any (give x…

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Q: 4. Consider the following triangle. a B b A a C Ö LL If A 39° and b= 15, find the values of: a. B b.…

A: Here use the properties of right triangle. And use the trigonometric formula for right triangle. The…

Q: Evaluate fff z dv, where E is the region bounded by 0≤x≤ 2, x-z≤ y ≤x+z, 0≤z ≤ x.

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Q: ii) Compute the work done by F(x, y) = (3x²y + 1,7³ − 2) along the curve parameterized by r(t) = (2…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: (a) Show that Q(√3, i) is a simple exension of Q by verifying that Q(√3, i) = Q(√3+ i). (b) Show…

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Q: Use the Laplace transform to solve the given system of differential equations. dx dt dy = 2x dt x(0)…

A: Given   dxdt = -x + y ------(1)                       dydt = 2x  ---------(2)…

Q: Find the area of the region. interior of r² = 49 cos(20)

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Q: Q2: Consider the following normed spaces (C([a,b]). Il-ll), (C¹([a, b]). lll.) and (C¹…

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Q: Here is a table showing all 52 cards in a standard deck. Face cards Suit Ace Two Three Four Five Six…

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A: A lattice path is made up of horizontal and vertical lines that run through the points of the…

Q: 77 n + e The limit of the sequence en12n + tan ¹(33 n) is e {in(₁ -48 n n=1 Hint: Enter the limit as…

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Q: Find the value of a for which the solution of the following IVP y"-y-2y = 0, y(0) = a, y'(0) = 13…

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