Let X ~ Gamma (8, 2) . Then E |[X²] is equal to

Q: (a) Show that y for the given z = e" In x+ xy

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Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: Find the critical number(s) of f(x) = sin x + cos(x) on the interval [0, 27].

A: i have solved question1 for next question please repost.

Q: let X~beta(a,b). find m.g.f ofY=ln| 1-x

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Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: (18) Verify by differentiation Va? + x² + c. 1 dx x² Va² + x² a²x

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

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Q: d Prove In Jax| dx In x for any constant a. dx

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Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

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Q: Demonstrate that for the integral of p(x)/q(x) where p(x) is of degree 2 and q(x) of degree 3 it is…

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Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

A: Given the statement

Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

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Q: Suppose X1 and X2 are iid observations from the pdf f(r|a) = ax 0. Show that (log X1)/(log X2) is an…

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Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: If the 2n RVs A, and B, are uncorrelated with zero mean and E(A²,) = E(B²,) = %3D o, show that the…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the…

A: suppose that y is an implicit function f(x) defined by the equationx3+y3=8xy−7. find the equation of…

Q: Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.19). L(x) =…

A: Here f(x)=lnx at x=1We have to find the linear approximation of f(x) andAlso find the value…

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

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

A: We can solve this as follows:

Q: If Y Poisson(A) and A has pdf f(A) = e-^ for A > 0, elsewhere, find zero E(2Υ) V (2Y):

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: If X ~ gamma(r, 1), show that the moment generating function of is given by if t < A. Mx(t) = { ()",…

A: Given, Mxt=λλ-tr As we know that, Ex=Mx'0Ex2=Mx''0 Now, Mx't=ddtλλ-tr=rλrλ-tr+1

Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

Q: Find the general anti-derivatives. (a) Evaluate ∫ xsin x dx

A: We use integration by parts

Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: Show that the family of functions {s()}" COS n=0 is mutually orthogonal on -L≤ x ≤ L, with respect…

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Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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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: Determine the expression of the integrating function if it is known that: e) S; f(x)dx : - sen(9) +…

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Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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

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Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: g(x) dx converges,

A: Observe the given graph carefully. Note that, in the interval [1,∞) the function g(x) forms a bigger…

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

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Q: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

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