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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2Fd337f6e7-e306-4b58-9295-e2d4945432cb%2F8ckm56c_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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].)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2Fd337f6e7-e306-4b58-9295-e2d4945432cb%2F2mvsunn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(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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