Question

fxy (x,y) dady. a) The probability of the event that 0 < Y < X <1 is of the form Find the values of a, b, c, d. Each one of your answers should be one of the following: 0, r, y, or 1. b= C= d = b) The probability of the event that 0 < Y < X < 1 is also of the form fx,y (r, y) dy dæ. Note the ( different order of integration as compared to part (a). Find the values of a, b, c, d. Each one of your answers should be one of the following: 0, x, y, or 1. a= b= C = d=

Answer 1

(a)  

$0\leq Y \leq X \leq 1$

So range of variation of X is,

Y I

Range of variation of Y is,

$0 \leq Y \leq X$

Given that,

fxy (x,y)d)dy

Here first integration is with respect to x and then with respect to y.

That means c = lower limit of x d = upper limit of x

a = lower limit of y b = upper limit of y

$\therefore$ a = 0

b = x

  c = y

d = 1

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(b)

$0\leq Y \leq X \leq 1$

So range of variation of X is,

Y I

Range of variation of Y is,

$0 \leq Y \leq X$

Given that,

fx,y (x, y)dy)dx

Here first integration is with respect to y and then with respect to x.

That means a = lower limit of x b = upper limit of x

c = lower limit of y d = upper limit of y

$\therefore$ a = y

b = 1

  c = 0

d = x

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