The relation between a and b for pdf shown below—

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The relation between a and b for pdf shown below—

1. ab = 1
2. ab = 0
3. ab = 2
4. ab = 3

Correct Option: A

Fx(x) =		b	x + b; x < 0
		a
		– b	x + b; x > 0
		a

Now, Fx(x) =		^∞	f x(x)dωx
		_{– ∞}

1 =

⁰

b

x + b

dx +

b

x + b

dx

_{– a}

a

a

or 1 =

b

x²

+ bx

⁰

+

– b

x²

+ bx

^a

a

2

_{– a}

a

2

₀

or 1 =	–ba²	+ ab –	b		a²	+ ab
	2a		a		2

or 1 =	– ab	+ ab –	ab	+ ab
	2		2

or 1 = ab