4.4-5. For each of the following functions, determine the value of c for which the function is a joint pdf of two continuous random variables X and Y. (a) f(x, y) = cxy, 05xs1, xsysx. 05xsysl. (b) f(x, y) = c(1 +x²y),

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Chapter1: Combinatorial Analysis
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4.4-5 a and b only

05XS7/2, 0SYST/2
0sysi,
10
144
y 2, be
(d) Are X and Y independent? Why or why not?
4.4
4.4-5. For each of the following functions, determine the
value of c for which the function is a joint pdf of two
continuous random variables X and Y.
ity density
ous
at? Why or
(a) f(x, y) cxy, 0sxs1, x sySx.
(b) f(x, y) = c(1 +x²y). 0sxs ysl.
05xsy, 0s ysl.
сху,
Dr
dY.
%3D
(а)
(c) f(x, y) = cye",
(d) f(x, y) = c sin(x+y).
(b)
%3D
(c)
4.4-6. Using Example 4.4-2,
(a) Determine the variances of X and Y.
(b) Find P(-X S Y).
show that
endent.
4.
ma
m
4.4-7. Let f(x, y) = 4/3, 0 <x < 1, <y< l, zero
th
elsewhere
Transcribed Image Text:05XS7/2, 0SYST/2 0sysi, 10 144 y 2, be (d) Are X and Y independent? Why or why not? 4.4 4.4-5. For each of the following functions, determine the value of c for which the function is a joint pdf of two continuous random variables X and Y. ity density ous at? Why or (a) f(x, y) cxy, 0sxs1, x sySx. (b) f(x, y) = c(1 +x²y). 0sxs ysl. 05xsy, 0s ysl. сху, Dr dY. %3D (а) (c) f(x, y) = cye", (d) f(x, y) = c sin(x+y). (b) %3D (c) 4.4-6. Using Example 4.4-2, (a) Determine the variances of X and Y. (b) Find P(-X S Y). show that endent. 4. ma m 4.4-7. Let f(x, y) = 4/3, 0 <x < 1, <y< l, zero th elsewhere
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