Let

f(x)

and

g(x)

be the probability density functions with corresponding cumulative distribution functions

F(x)

and

G(x)

, respectively. With

c

denoting a numerical constant satisfying

|c|

, consider\

h(x,y)=f(x)*g(y)*{1+c*[2F(x)-1]*[2G(y)-1]}

\ a. Please proof that

h(x,y)

is a well-defined joint density function.\ b. Let

A

and

B

be the random variables with joint density function

h(x,y)

. Please find the density functions of

A

and

B

, respectively.\ c. Please find the value of

c

such that

A

and

B

are independent.

Let f(x) and g(x) be the probability density functions with corresponding cumulative distribution functions F(x) and G(x), respectively. With c denoting a numerical constant satisfying c