Let X and Y be two random variables. The relationship $E (X Y) = E (x) \cdot (Y)$ holds.

Always

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E (X + Y) = E (X) + E (Y)

is true

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X

and

Y

are independent

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X

can be obtained from

Y

by a linear transformation

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Solution

The correct option is B If $X$ and $Y$ are independent
$E (X Y) = E (X) \cdot E (Y),$ if $X$ and $Y$ are independent.

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Similar questions

Q. The general solution of the differential equation

\frac{d y}{d x} = e^{x + y}

, is
(a) e^x+ e^−y = C
(b) e^x + e^y = C
(c) e⁻^x + e^y = C
(d) e^−x + e^−y = C

Q. If

e^{x} + e^{y} = e^{x + y}

, prove that

\frac{d y}{d x} + e^{y - x} = 0

Q. If

e^{x} + e^{y} = e^{x + y}

, show that

\frac{d y}{d x} = - e^{y - x}

The general solution of the differential equation $\frac{d y}{d x} = e^{x + y}$ is
(a) $e^{x} + e^{- y} = C$
(b) $e^{x} + e^{y} = C$
(c) $e^{- x} + e^{y} = C$
(d) $e^{- x} + e^{- y} = C$

Q. If

e^{x} + e^{y} = e^{x + y}

, prove that

\frac{d y}{d x} + e^{y - x} = 0

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Let X and Y be two random variables. The relationship E(XY)=E(x)⋅(Y) holds.

The correct option is B If X and Y are independentE(XY)=E(X)⋅E(Y), if X and Y are independent.

Let X and Y be two random variables. The relationship $E (X Y) = E (x) \cdot (Y)$ holds.

The correct option is B If $X$ and $Y$ are independent
$E (X Y) = E (X) \cdot E (Y),$ if $X$ and $Y$ are independent.