5

11. Show that the density function of the t distribution with n degrees of freedom is t2 (n+1)/2 TIn + 1)/2] f(t) = 1 + VnnT (n/2)...

Question

11. Show that the density function of the t distribution with n degrees of freedom is t2 (n+1)/2 TIn + 1)/2] f(t) = 1 + VnnT (n/2)

11. Show that the density function of the t distribution with n degrees of freedom is t2 (n+1)/2 TIn + 1)/2] f(t) = 1 + VnnT (n/2)



Answers

Show that the function is a probability density function on the show that the function is a probability density function on the specified interval. $$f(x)=\frac{12-x}{72} ;(0 \leq x \leq 12)$$

All right. So say we're given a density function that we want we want to see. Ah, we want to show that the mean of this density function is infinite. So to do that, we take the function over the, uh, interval. Um, and we do x times. The function that gives us that gives us the mean value. Um, since we're taking the weight, which is two over to over pi expert, plus one times the, uh, the value which is just acts. And that should give us the mean value, the value times the weight of that value. So to do this integral, this one's not too bad. So where you just take the two of her pie out, and then this looks a lot just like Ellen of X squared plus one. But if we took the derivative A to X would come out. Not just the next. So we need Thio. We need to put in an extra half so and then this gets evaluated from zero to infinity and the twos can cancel out. So the ellen over pie Helen over by one over by times ln of x squared plus one. So infinity squared plus one minus one over pi times, Ellen of zero squared plus one. So, Ellen, one which is zero. So this part goes away. And this beverages since Ellen of infinity, uh, just blows up. So, yes, this this function has an infinite mean.

Given the function one day four x or the interval. One country. So we're probably too. Then the area off the function under this interval should be equal to one. So let's verify this. Integral. 123 It affects the X is equal to Bill. Okay, Okay, okay. Is equal to one, sir clarifies the second property.

Given the function effect is equal to X or they endured. You're the one you need to verify. Their second property is obeyed. The second property is there 80 other functional. The interval should be equal to one. Let's calculate the area or this in double. Okay, Okay. Okay. Physical one. So probably do is verified.

So the probability density function given is three or the n double zero comma one day three. No way to verify the second property, which is the states that area. Another interval or the function should be equal to one that is the area 02 one way three effects. The X should be called one. The less gavel into Syria is equal one. So property It was very fair.


Similar Solved Questions

2 answers
Consider the following set of ordered pairs shown below Assuming that the regression equation is % = 357 0.643x and the SSE = 3.857 ccnstruct 90% coniidence interva for x =5.Click the icon to view portion of the Students t-distribution tableCalculate the upper and lower Iimits of the confidence interval:UCLLCL
Consider the following set of ordered pairs shown below Assuming that the regression equation is % = 357 0.643x and the SSE = 3.857 ccnstruct 90% coniidence interva for x =5. Click the icon to view portion of the Students t-distribution table Calculate the upper and lower Iimits of the confidence in...
5 answers
Question 3The cpithelium of the anal canal is thc samc as that of the colonTrueFalse
Question 3 The cpithelium of the anal canal is thc samc as that of the colon True False...
5 answers
Point) Determine the &gn 0t f , and f , at each indicated point uslng the contour diagram ot showm berow: (Tha point P tat In ine first quadran positva and value; Q through T are located ckckwiisa from P , s0 that Q at a positive value and negatve Y, etc )Al pomt 0 _ [email protected] At pont
point) Determine the &gn 0t f , and f , at each indicated point uslng the contour diagram ot showm berow: (Tha point P tat In ine first quadran positva and value; Q through T are located ckckwiisa from P , s0 that Q at a positive value and negatve Y, etc ) Al pomt 0 _ positive @i At pont...
5 answers
Point) Suppose f(w) is continuous function defined on 00O with exactly twO critical points. Which of the following statements are true?Check all that are true A f(z) may have global maximum at more than one €-value flc_ cannot have any global extrema c f(z may or may not have global extrema D: f(r may have global minimum or global maximum; but cannot have both E f(r) must have both global maximum and global minimum
point) Suppose f(w) is continuous function defined on 00 O with exactly twO critical points. Which of the following statements are true? Check all that are true A f(z) may have global maximum at more than one €-value flc_ cannot have any global extrema c f(z may or may not have global extrema ...
3 answers
Problem (6.& #2 and #3)_ Let € = C (1) be the circle in the complex plane centered at with radius oriented counterclockwise_ Use Cauchy' integral formulas tO evaluate the integralsand(2+1)(2 - 1)(2+1)(2 - 1)2Note; Solutions that do not use Cauchy s integral formulas will not receive credit. Such solutions also sound likc t0o much WOr<, Also. be sure tO justify that the integral formula yOu use applies to your given integral.
Problem (6.& #2 and #3)_ Let € = C (1) be the circle in the complex plane centered at with radius oriented counterclockwise_ Use Cauchy' integral formulas tO evaluate the integrals and (2+1)(2 - 1) (2+1)(2 - 1)2 Note; Solutions that do not use Cauchy s integral formulas will not recei...
5 answers
Consider the following catalytic cycle:NH3 H3N-_Ni= 'NH3Ph NH3 Cl-_Ni: NH3 NH3Ph_NH3 Ni NH3HCICl , NHz Ni Ph- NH3Ph NH3 CI Ni NH3Ph Cl , NH3 Ni NH3Cl/,_ NH3 Ni NHgGive an appropriate name for each step of the reaction (i.e. A 7 B is called "X"): [7 marks]NH3
Consider the following catalytic cycle: NH3 H3N-_Ni= 'NH3 Ph NH3 Cl-_Ni: NH3 NH3 Ph_ NH3 Ni NH3 HCI Cl , NHz Ni Ph- NH3 Ph NH3 CI Ni NH3 Ph Cl , NH3 Ni NH3 Cl/,_ NH3 Ni NHg Give an appropriate name for each step of the reaction (i.e. A 7 B is called "X"): [7 marks] NH3...
5 answers
FindFH 2 dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,3,0), and (0,0,4)Question Help:VideoVideo 2Message instructorSubmit Question
Find FH 2 dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,3,0), and (0,0,4) Question Help: Video Video 2 Message instructor Submit Question...
5 answers
Question 8pathways between the host and the microbe: True or False The best antimicrobial drugs target commonTrueFalse
Question 8 pathways between the host and the microbe: True or False The best antimicrobial drugs target common True False...
1 answers
Use the special products of this section to determine the products. You may need to write down one or two intermediate steps. $$(x-y)(x+y)\left(x^{2}+y^{2}\right)$$
Use the special products of this section to determine the products. You may need to write down one or two intermediate steps. $$(x-y)(x+y)\left(x^{2}+y^{2}\right)$$...
5 answers
Suppose you drop a rock from the top of a 400 -foot-high building. Express the distance $D$ from the rock to the ground as a function of time $t .$ What is the range of this function? [Hint: See Example 3.]
Suppose you drop a rock from the top of a 400 -foot-high building. Express the distance $D$ from the rock to the ground as a function of time $t .$ What is the range of this function? [Hint: See Example 3.]...
5 answers
'Jo hnd tha volume the solid obtalned {Ocalin- the reglan cnclosed cre method and rotate vertical 4ma 4rouno cheIlne creaund cylindarMe Vee Vle-Cyllnuneaneaund Fright"Taeennnvolume can be found (rom thc intcaral
'Jo hnd tha volume the solid obtalned {Ocalin- the reglan cnclosed cre method and rotate vertical 4ma 4rouno cheIlne creaund cylindar Me Vee Vle-Cyllnuneanea und Fright" Taeennn volume can be found (rom thc intcaral...
5 answers
Let z=ex2y, where x=uv−−√ and y=1v.Find ∂z∂v in terms of u and v.
Let z=ex2y, where x=uv−−√ and y=1v. Find ∂z∂v in terms of u and v....
5 answers
(#3-9J: (a) Approximate fby a Taylor Polynomial with degree atthe number (b) Use Taylor' $ Inequality- to estimate the accuracy of the approximation f (+)~T;(x)when lies in the given interval (c) Check your result in part (b) by graphing Ir (r):flx)=+5, a =4 n=2 4<*<4.2f(x) =x a=l n=3, 0.8<*<1.2f() =secx; 0 =n=20.2<*<0.2
(#3-9J: (a) Approximate fby a Taylor Polynomial with degree atthe number (b) Use Taylor' $ Inequality- to estimate the accuracy of the approximation f (+)~T;(x)when lies in the given interval (c) Check your result in part (b) by graphing Ir (r): flx)=+5, a =4 n=2 4<*<4.2 f(x) =x a=l n=3, ...
5 answers
3. Give the IUPAC name for the followng compound:4. Give the IUPAC name for the followng compound:OHOH
3. Give the IUPAC name for the followng compound: 4. Give the IUPAC name for the followng compound: OH OH...
5 answers
(d} Write out the automatically defined classes and construct cumulative these classes (Round your closs answyers t0 decimal place )walting time usingGurnanannn FroquuncyClass
(d} Write out the automatically defined classes and construct cumulative these classes (Round your closs answyers t0 decimal place ) walting time using Gurnanannn Froquuncy Class...
5 answers
14. (5 pts ) Use Newton'$ method to estimate the one real solution of x' +3x+l=0_ Start with Xo = 0 and then find Xz
14. (5 pts ) Use Newton'$ method to estimate the one real solution of x' +3x+l=0_ Start with Xo = 0 and then find Xz...
5 answers
4: (10 marks) Let G be a group (not necessarily Abelian) . Prove the following about the groupFor a,b elements of G; if (a * b)2 = a2 * b2, then a * b = b * a_
4: (10 marks) Let G be a group (not necessarily Abelian) . Prove the following about the group For a,b elements of G; if (a * b)2 = a2 * b2, then a * b = b * a_...

-- 0.018911--