(a) Determine the marginal cumulative distribution functions of X and Y. (b) Determine the marginal probability mass functions of X and Y. Do you recognize one of the standard probability distributions? (c) Determine the joint probability mass function of X and Y. (d) Are X and Y independent? Do this after the 10/10 lecture

MATLAB: An Introduction with Applications
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7. Suppose that the joint cumulative distribution function of X and Y is given by
F(a,b) = 1 − 4¯la] 2 - [b]
+2-²[a]-[¹] if a > 0 and b > 0,
=
0 otherwise. Here [x] is the largest integer smaller or equal to x ('rounding
and F(a,b)
down').
(a) Determine the marginal cumulative distribution functions of X and Y.
(b) Determine the marginal probability mass functions of X and Y. Do you recognize one of
the standard probability distributions?
(c) Determine the joint probability mass function of X and Y.
(d) Are X and Y independent? Do this after the 10/10 lecture
Transcribed Image Text:7. Suppose that the joint cumulative distribution function of X and Y is given by F(a,b) = 1 − 4¯la] 2 - [b] +2-²[a]-[¹] if a > 0 and b > 0, = 0 otherwise. Here [x] is the largest integer smaller or equal to x ('rounding and F(a,b) down'). (a) Determine the marginal cumulative distribution functions of X and Y. (b) Determine the marginal probability mass functions of X and Y. Do you recognize one of the standard probability distributions? (c) Determine the joint probability mass function of X and Y. (d) Are X and Y independent? Do this after the 10/10 lecture
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