16. Show that for the chi-square distribution 1 2 2. 1 f (x³) d (x³) = X (x) e 2n/2 r n/2 H (about the origin)=n (n+ 2) (n+4)...(n + 2r – 2).

Q: 1. Which of the following is incorrect? a. b. [(f(x) · g(x)) dx = [ f(x) dx . [ g(x) dx [(f(x) +…

A:

Q: Let X ∼ Poisson(λ) where f(0) = f(1). (a) Use the given condition to find λ (b) Solve for x if (x −…

A: a) The probability mass function for X is, fX=x=e-λλxx! Given f(0)=f(1) fX=0=fX=1e-λλ00!=e-λλ11!…

Q: 1) y = Vx2 – 4 2) y = x²Vx3 – 1 3) y = (4x²Vx3) 4) y = x3 + 2x2 – x + 1 5) y = 5x3

A: If y=f(x)n ⇒y'=nf(x)n-1f(x)' We know ddxxn=n xn-1

Q: Find f"(x). f(x) = (x² + 1) * %3D f"(x) = %3D

A: Given Data: Function: f(x)=(x2+1)4 The first derivative of the given function is,…

Q: -= In[F(x)]+C. What is f(3) if C= 0? (x+x³) (x Tan-'x+1) A 3 B 6. 3 D V3 6 . + + -1/5

A:

Q: 12 If [" f(x) dx = 19 and ' [₁ f(x) dx [R²F(x) f(x) dx = 4, find the following.

A: We can answer the question as below using the properties of definite integral.

Q: If g(4) = 3 and gʻ(x) > –6.5 for all x E [4,6], what is the smallest possible value of g(6)?

A:

Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: 2. the approximated roots for equationf(x) = e* - 3x in intervals [1,3] is found to be 1.34 find the…

A:

Q: -5(x – 4)e8x (x + 5)7 f'(x)

A:

Q: 2.2 Given f(x) dx = 10 and ſº g(x) dx = −2, evaluate [g(x) = f(x)] dx b. [f(x) + g(x)] dx ₂2g(x) dx…

A:

Q: x² e=a* {H„(x)}® dx = (Vn)2*n!(n + }).

A:

Q: 3. [FTC3.12] Suppose f(x) dx = −9, -9, 8(x) dx = 5, and [ f(x) dx = 3. (8f(x) + 2g(x)) dx. Show all…

A: Suppose ∫-54 fx dx=-9, ∫14gx dx=5, and ∫-51 fx dx=3. To find the value of ∫148fx+2gx dx.

Q: 1. (a) Evaluate Jo 0 r* - ¹ (1 − x6) 15 (1+x) ¹5 -dx.

A:

Q: 2. Let X denote the amount of space occupied by an article placed in a 1 - fr' packing container.…

A:

Q: 15 6. 15 | f(x)dx = 8, 6. Suppose f(x)dx = 1, 9, f(x)dx = 4. %3D 12 12 f(x)dx = 3 6, 6. (8f(x) –…

A: Given, ∫912f(x)dx=3 To find ∫129(8f(x)-1)dx.

Q: 1 Let g(x) = 2+3Vr. Prove that gl exists, and find (g)'(5). %3D

A:

Q: 1. Plot the function f(t)= (x+5) for -35 x 3. 4+3x2

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

Q: 2. Let g(x) = "(x² – 4x + 6) dx. Is the graph of g concave up or concave down at x 1? Justify your…

A: Explanation of the answer is as follows

Q: Let f(x) =7 (1 + x*y/" for n22 and g(x) = (fofo.f) (x). Then Jx"-g (x) dx f occurs n times equals…

A:

Q: 2. The graph of g(x), is shown below with 7 points noted along the curve. Mark these points A - G…

A: The graph of g(x), is shown below with 7 points noted along the curve. To Mark these points A-G…

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

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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: 19 The value of f(x) dx by using 2-segment Simpson's 1/3 rule is estimated as 702.039. The 3…

A:

Q: 13.5 Suppose *** f(x) dx = 2, S 6 11 8.5 f(x) dx = 8.5 * ( 2 f(x) - 4) dx = 11 8.5 √5³ f(a)dx = 4, 6…

A:

Q: 3. [15] The following data can be used to approximate the integral M sin(a²) dr. N(h) = 2.50663, Ni…

A: Given, M=∫0πsinx2dxN1h=2.50663N1h2=1.66875N1h4=0.88018N1h8=0.88894To find: N4h

Q: f(x) = + In(x) exp(x) + exp(-x) herex e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into…

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

Q: Given L f(x) dx = 16 and i g(x) dx = 8, Evaluate the following I [2f(x) - 3g(x)] dx

A: Given query is to find the value of the indicated integral.

Q: (a) f(x) = x(Kx+1); I<x<2 -%t f(x) = Kx² - ; 1<x<2 % (c) f(x) = Kx; 0<x<2 (d) f(x) = K(x² +4); 0<x…

A: As per our guidelines we are suppose to answer three sub parts.

Q: S ³f(x) dx = 5, ³g(x) dx = 7, and Which of the following can be determined given Ⓒ S (f(x) - g(x))…

A: We have to solve integral

Q: 1. The E (]x – µ|²) is equivalent to St(x - 4)? f(x)dx + S"(x – 4)²f(x)dx . True O False

A: Solution

Q: 11

A:

Q: 29-62. Definite integrals Evaluate the following integrals using the Fundamental Theorem of…

A:

Q: 1 S² F(x) '9 +6² f(x) dx = 37 and g(x) dx= 18, find I' [3f(x) + 5g(x)] dx.

A:

Q: RV X with pdf f(x) = cx², -1 0) 2. P(X>0|X< 1) 3. P(X<1| X <0) I.

A: Given that Pdf of X is  f(x)=cx2, -1&lt;x&lt;2 Note: According to bartelby question answer…