3. The following equations are incorrect since the r.h.s. is unfinished. Pleaseadd whatever is appropriate to the r.h.s. so that the equations hold. Assumethat (X, Y) have joint p.d.f. fx,y (s, t).(a)(b)(c)(d)(e)1 = fx,y (s, t)Fx,y(u, v) = fx,y (s, t)fx(s) = fx,y (s, t)E[X] = fx(s)E[g(X,Y)] = fx,y(s, t) (f)(h)(i)(j)fy(t) = fx,y (s, t)fx|Y=t(s) = fx,y (s, t)E[X | Y = t] = fx\Y=t(S)E[X² | Y = t] = fx\Y=t(S)E[E[X | Y]] = E[X | Y = t](In the above, you should be thinking of E[X | Y] as a function of Yand applying LOTUS. BTW, E[E[X | Y]] = E[X].)

The equations of the RHS are incorrect for the given question. The objective is to set the correct…

3. The following equations are incorrect since the r.h.s. is unfinished. Please add whatever is appropriate to the r.h.s. so that the equations hold. Assume that (X, Y) have joint p.d.f. fx,y (s, t). (a) (b) 1 = fx,y (s, t) Fx,y(u, v) = fx,y (s, t) fx(s) = fx,y (s, t)

3. The following equations are incorrect since the r.h.s. is unfinished. Please add whatever is appropriate to the r.h.s. so that the equations hold. Assume that (X, Y) have joint p.d.f. fx,y (s, t). (a) (b) 1 = fx,y (s, t) Fx,y(u, v) = fx,y (s, t) fx(s) = fx,y (s, t)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 70E

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Question

3. The following equations are incorrect since the r.h.s. is unfinished. Please
add whatever is appropriate to the r.h.s. so that the equations hold. Assume
that (X, Y) have joint p.d.f. fx,y (s, t).
(a)
(b)
(c)
(d)
(e)
1 = fx,y (s, t)
Fx,y(u, v) = fx,y (s, t)
fx(s) = fx,y (s, t)
E[X] = fx(s)
E[g(X,Y)] = fx,y(s, t)

(f)
(h)
(i)
(j)
fy(t) = fx,y (s, t)
fx|Y=t(s) = fx,y (s, t)
E[X | Y = t] = fx\Y=t(S)
E[X² | Y = t] = fx\Y=t(S)
E[E[X | Y]] = E[X | Y = t]
(In the above, you should be thinking of E[X | Y] as a function of Y
and applying LOTUS. BTW, E[E[X | Y]] = E[X].)

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