5. The amplitudes of two signals \(X\) and \(Y\) have joint pdf:
$$ f_{X, Y}(x, y)=k x(1-x) y, \text { for } x, y \in(0,1) \text { . } $$
(i) Find the \(k\) and the joint CDF.
(ii) Find the marginal pdfs and CDFs.
(iii) Find \(P\left[Y<X^{1 / 2}\right]\).
Homework Answers
CONCEPT:-
FIND THE VALUE OF k
SKETCH THE CURVE OF Y=SQRT(X)
DEFINE THE RANGE OF X AND Y USING GRAPH
INTEGRATE THE JOINT PDF ON DEFINED RANGES
YOU WILL GET THE ANSWER
ALL CALCULATION ARE GIVEN AS BELOW
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