X and Y are independent random variables and they have the s

X and Y are independent random variables and they have the same density function (a) Find the value of the constant c. (b) Find the value of P(Y

Solution

f(x) = c(2-x)

Integrate f(x) from 0 to 1 and equate to 1

c(2x-x^2/2)Substitutw 0 and 1

=3c/2 =1

or c = 2/3

b) P(Y<=2x) = 4x-2x^2,

c) As continuous variable answer the same as b.