let x has the p.d.f 0 < x < 0 O. W 13е-13х f(x) = Find m.g.f and prove that E(x) = M,(0)?

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

A: We have to find the value of delta(d) in terms of x0 and e while evaluating the limit at x := x0 for…

Q: Find f(x) if f(4) = -8 and the tangent line at (x , f(x)) has slope 7o* + 4. O a. f(x)= 7e* + 4x –…

A:

Q: The function if x E Q is 0 if x E R \Q continuous at every x E R. 1 f(x) =

A:

Q: Let g(t) be piecewise continuous on [0, ∞) and of exponential order, use the convolution theorem to…

A:

Q: Q2. Let f:R- R be a function such that f(x) = x sin| f is defined at x, , where the value of d…

A: Topic- Limits

Q: e that f(x) is continuous, and f'(x) is given in the figure below. y y = f'(x) 1 3

A: In this question we will use basic of calculus i.e concept of maximum and minimum. Solution of the…

Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

A:

Q: Let L{f(t)} F(s) and is a real constant. Then, 27- L{F(s-a)} =? On taf(t) OD f(at) Oo t"f(t) OD e…

A:

Q: If f is a piecewise continuous and T-periodic, then show that for a e R T ra+T f (x) dx = - (2) f…

A: i used the change of variable formula to obtain solution

Q:

A: We have given geometric distribution and two statistics associated with it and we have to check…

Q: In the following cases, show that the p.d.f. of Y is not a member of complete family. 1. Y: N (0,…

A: A test statistic is said to belong to the family of completeness only when it follows the conditions…

Q: (e) If f(x) is reducible over Q then f(x +a) : a E Z is reducible over Q.

A:

Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

A:

Q: (a) Let X have the following pdf : S2(x - 1) 1<z<2 S(2) = elsewhere. Compute E(X'), E(2X-1)

A: As per our guidelines we are suppose to answer first question.

Q: Let f(x, y) = cos(xev*) + cos(x + ey²) , find дхду* O a. -2ye" (sin(xe") – x cos(xev*) + cos(x +…

A:

Q: use the definition to find the derivetive of feconction fcx) = 「X+/ and obtain Hりe equabion of ナんe…

A:

Q: Suppose f E R[0, 1] and let f() in An k=1 for all n. Prove that an → So f dx.

A: Given -  To Prove -

Q: Let f(x) = x – x³ on [0, 1]. f(0) f(1) = Find c such that f'(c) = 0 or, if Rolle's Theorem does not…

A:

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

A:

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

A:

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: 1 Let f(x) = 8 + In (t) dt, for x2 1. Find f'(2).

A:

Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

A:

Q: let x has the p.d.f (11e-11x 0 < x< ∞ 0. W f(x) = Find m.g.f and prove that E(x) = M,(0)? %3D

A: We want to find the Mx(t) and E(x)

Q: Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both…

A: Given: Suppose ϕ(t) is a differentiable function with ϕ'(t)≤kϕ(t) (k&gt;0) such that ddtϕ(t)e-kt≤0.…

Q: Suppose that T(X) is sufficient for 0 and that ^e(X) is an MLE of 0. Show that ^0 depends on X…

A:

Q: Let y = f(x) be an positive increasing function defined for x > 0. The length of the curve described…

A: Given:         Length of curve y=f(x) is between x=0 and x=t is equal to14t4+t2+lnt+4+t2−ln2.

Q: Suppose that F(s) = ℒ{f(t)} exists for s &gt; a ≥ 0. Show that if k is a positive constant, then…

A:

Q: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

A: A function is even if f(-x)=f(x)

Q: 7. Suppose that X and Y have a continuous joint distribu- tion for which the joint p.d.f. is as…

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

Q: has a limit at xo + 0. If Q2. Let f:R → R be a function such that f(x) x sin f is defined at xo,…

A:

Q: In the following cases, show that the p.d.f. of Y is not a member of complete family. 1. Y: N(0, o²)…

A: For any statistics to be a complete statistics it must satisfy the following conditions i) E(x(t)) =…

Q: Suppose that f(x, t) is the probability of getting x suc-cesses during a time interval of length t…

A:

Q: If f is defined at x = a, then | f(x)dx is equal to O 1 O a O-a

A:

Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

A:

Q: 50 if x E Q 1 if x € R\ Q Let f(x)= Prove that y=f(x) is not continuous at any points a E IR.

A: Take p ∈ Q and let (xn) be a sequence of irrationals converging to p. Then f (p) = 1 but f (xn)→ 0…

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: Let f be the function defined on [0, 1] by when x is irrational, f (x) = 1 when x is rational.…

A: Please see the below picture for detailed solution.

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

A:

Q: If F is an antiderivative of f, then which other function is guaranteed to be an antiderivative of…

A: If F(x) is antiderivative of f(x) then F(x)+C (where C is a constant), is also an antiderivative of…

Q: Suppose f(z) = (z – i)³e² is analytic inside and on circle |z – i| = 3. Then the upper bound of…

A: Given that f(z)=(z-i)3ez- is analytic inside and on the circle|z-i|=3To find the upper bound of…

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A:

Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

A:

Q: Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following…

A: We have to find L(x).