Question

if r =0.4, cov(x,y) =10 and S. d of y is 5 the sd of x is​

Answer 1

The value of S.d (x) is equal to 5.

Given that;

r =0.4, cov (x,y) =10 and S.d of y is 5

To find;

The S.d of x

Solution;

We know that,

r(x,y) = $\frac{cov(x,y)}{\sqrt{var x . vary} }$...(1)

It is given that,

S.d of y = 5 therefore,

var(y) = $[S.d(y)] ^{2}$

var(y) = 25

Putting all the given values in equation (1) we get,

0.4 = $\frac{10}{\sqrt{var(x) . 25} }$

squaring both sides we get,

0.16 = $\frac{100}{var(x) . 25}$

var(x) = $\frac{100}{0.16 X 25}$

var(x) = 25

As we know,

standard deviation = $\sqrt{variance}$

S.d(x) = $\sqrt{var(x)}$ = $\sqrt{25}$ = 5

Hence, the value of S.d (x) is equal to 5.

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Answer 2

Answer: Hence, the value of S.d (x) is equal to 5.

Step-by-step explanation:

So, here we need to do the cov(x,y)

And we get the total idea of all the cov(x,y):-

The formula is: Cov (X,Y) = Σ E ((X – μ) E (Y – ν)) / n-1 where: X is a random variable E (X) = μ is the expected value (the mean) of the random variable X and we get an idea of the of the cov(x,y) via the formula experimental.

The value of S.d (x) is equal to 5.

Given that;

r =0.4, cov (x,y) =10 and S.d of y is 5

To find;

The S.d of x

Solution;

We know that,

r(x,y) = ...(1)

It is given that,

S.d of y = 5 therefore,

var(y) = 25

Putting all the given values in equation (1) we get,

0.4 =

squaring both sides we get,

0.16 =

var(x) =

var(x) = 25

As we know,

standard deviation =

S.d(x) =  =  = 5

Hence, the value of S.d (x) is equal to 5.

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