Suppose E(X) = 5 and E[X(X − 1)] = 27.5. (a) What is E(X2)? [Hint: First verify that E[X(X − 1)] = E[X2 − X] = E(X2) − E(X).] (b) What is V(X)? (c) What is the general relationship among the quantities E(X), E[X(X − 1)], and V(X)?

Q: Suppose f and g are differential functions with the values given below. f(x) f'(x) g(x) g'(x) 1 1 3…

A: The answer is found in step-2

Q: for every choice of the constant c, the function x =( K ) / ( 1+ce−rt ) is a solution of the…

A:

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

A:

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: Find f(x) by solving the initial-value problem. f '(x) = 6ex − 10x; f(0) = 15

A:

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: x-1, X)1 find the generol solution of the differential eguation below

A:

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: Obtain a differential equation associated with the primitive Ax2 + By2 = 1

A: See answer below.

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

A:

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

A: Note: Since you have posted a question with two subparts, we will solve the first part for you.…

Q: f'(x) = cos x; y (G) = 3 %3D

A:

Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: |- find the general Solestion of the differential eq ladich

A: Note : According to company guidelines we can solve only first question. So please post other…

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: X₁ and X₂ are random samples from exp(). when x > 0.) (pdf of exp()=e Determine the constant c so…

A: we have given that Xi follow exponential with mean λ that is E(Xi) = λ also, X1 and X2 are…

Q: Based on a study, the Lorenz curves for the distribution of incomes for bankers and actuaries are…

A: Given: Lorenz curve for the distribution of incomes for bankers, fx=110x+910x3. Lorenz curve for…

Q: at

A:

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N =…

A:

Q: Find the equation of the curve whose slope at any point is equal to 1+y/(x ln⁡x )-1/ln⁡x and which…

A: We have to find the equation of the curve whose slope at any point is equal to 1+yx ln x-1ln x and…

Q: The value of x2 in the given equation of f(x) = x3 + cos(x) would be equal to initial value of -1…

A: The given problem is to find the value of x2 for the given function with given initial values Given…

Q: Differentiate the following

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find f(x) by solving the initial-value problem. f '(x) = 8ex − 4x; f(0) = 12

A:

Q: X and Y are exponentially distributed and independent with densities f(x)=-exp| a a X Obtain P X +Y

A: 8. From the given information, X and Y are exponentially distributed and independent.…

Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: 1. Discuss in detail the connections between differential and integral calculus.

A:

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: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: {fn(x)}1 converges a.e. to a function f(x) to be determined.

A:

Q: 98x2.1for one year to y

A:

Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A: Given: Lorenz curve for first year: y = 0.97x2.1 And for the next year: y = 0.35x2 + 0.65.

Q: With an assumption that an insect population grows continuously and the rate of growth is…

A:

Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

A:

Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Example 8.19. Use Romberg's method to compute dx 1 + x² correct to 4 decimal places.

A: Let y = 11+x2  and let I = ∫01dx1+x2take h = 0.5 =12The tabulated values of y are   x0 x1 x2 x…

Q: Determine whether each of the following statements is true or false, and explain why.To determine a…

A: Given- To determine a particular solution to a differential equation, you first must find a general…

Q: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

A:

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

A:

Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

A: