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If Z = aX + bY and r is the correlation coefficient between X and Y, then $sigma subscript z superscript 2$ is equal to -

$a^{2} σ_{x}^{2} + b^{2} σ_{y}^{2} + 2 a b r σ_{x} σ_{y}$
$a^{2} σ_{x}^{2} + b^{2} σ_{y}^{2} - 2 a b r σ_{x} σ_{y}$
$2 a b r σ_{x} σ_{y}$
None of these

The correct answer is: $2 a b r sigma subscript x end subscript sigma subscript y end subscript$

To find the variance of z.
$v a r left parenthesis a x plus b y right parenthesis equals a squared v a r left parenthesis x right parenthesis plus 2 a b space c o v a r i a n c e left parenthesis x comma y right parenthesis plus b squared v a r left parenthesis y right parenthesis r equals fraction numerator c o v a r i a n c e left parenthesis x comma y right parenthesis over denominator square root of v a r left parenthesis x right parenthesis end root square root of v a r left parenthesis y right parenthesis end root end fraction v a r left parenthesis x right parenthesis equals sigma subscript x squared comma space v a r left parenthesis y right parenthesis equals sigma subscript y squared c o v a r i a n c e left parenthesis x comma y right parenthesis space equals r sigma subscript x sigma subscript y v a r left parenthesis z right parenthesis equals sigma subscript z squared equals a squared sigma subscript x squared plus 2 a b r sigma subscript x sigma subscript y plus b squared sigma subscript y squared$

Therefore, var(z) = $a to the power of 2 end exponent sigma subscript x end subscript superscript 2 end superscript plus b to the power of 2 end exponent sigma subscript y end subscript superscript 2 end superscript plus 2 a b r sigma subscript x end subscript sigma subscript y end subscript$

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If Z = aX + bY and r is the correlation coefficient between X and Y, then is equal to -

None of these

The correct answer is:

To find the variance of z.

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If Z = aX + bY and r is the correlation coefficient between X and Y, then $sigma subscript z superscript 2$ is equal to -

$a^{2} σ_{x}^{2} + b^{2} σ_{y}^{2} + 2 a b r σ_{x} σ_{y}$
$a^{2} σ_{x}^{2} + b^{2} σ_{y}^{2} - 2 a b r σ_{x} σ_{y}$
$2 a b r σ_{x} σ_{y}$
None of these

The correct answer is: $2 a b r sigma subscript x end subscript sigma subscript y end subscript$

The imaginary part of $fraction numerator e to the power of i theta end exponent over denominator 1 minus k e to the power of i phi end exponent end fraction$ is-

The imaginary part of $fraction numerator e to the power of i theta end exponent over denominator 1 minus k e to the power of i phi end exponent end fraction$ is-

If the lines $x to the power of 2 end exponent plus 2 x y minus 35 y to the power of 2 end exponent minus 4 x plus 44 y minus 12 equals 0$ and $5 x plus lambda y minus 8 equals 0$ are concurrent, then the value of l is

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If the equation $a x to the power of 2 end exponent plus 2 h x y plus b y to the power of 2 end exponent plus 2 g x plus 2 f y plus c equals 0$ represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is

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The point of intersection of the straight lines represented by $6 x to the power of 2 end exponent plus x y minus 40 y to the power of 2 end exponent minus 35 x minus 83 y plus 11 equals 0$

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The distance between the parallel lines $x to the power of 2 end exponent plus 2 square root of 2 x y plus 2 y to the power of 2 end exponent plus 4 x plus 4 square root of 2 y plus 1 equals 0 text is end text$

The distance between the parallel lines $9 x to the power of 2 end exponent minus 6 x y plus y to the power of 2 end exponent plus 18 x minus 6 y plus 8 equals 0 text is end text$

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The equation to the pair of lines through the origin perpendicular to the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 10 x plus 5 y equals 0 text is end text$

The equation to the pair of lines through the origin perpendicular to the pair of lines $2 x to the power of 2 end exponent plus 5 x y plus 2 y to the power of 2 end exponent plus 10 x plus 5 y equals 0 text is end text$