Find the Variance

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  • #1
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is known that the Tomato crop (in ton) in some farm are Sampled for 10 years.
the Standard deviation of the crop was 2 ton.
the Income (Y) from the Tomato Depends on the crop (X)
according to following connection Y=3X-2 the Variance Income from the Tomato in this Sampled is 4?

if i know that the Standard deviation is 2 so i just need to do 2^2 to get the Variance yes?

and 1 more Question: the Value of Pearson product-moment correlation coefficient between the crop and the Income is?
how i can solve it?

thanks for help.
 

Answers and Replies

  • #2
vela
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is known that the Tomato crop (in ton) in some farm are Sampled for 10 years.
the Standard deviation of the crop was 2 ton.
the Income (Y) from the Tomato Depends on the crop (X)
according to following connection Y=3X-2 the Variance Income from the Tomato in this Sampled is 4?

if i know that the Standard deviation is 2 so i just need to do 2^2 to get the Variance yes?
If you're referring to var(Y), then no, it isn't equal to 4.
and 1 more Question: the Value of Pearson product-moment correlation coefficient between the crop and the Income is?
how i can solve it?

thanks for help.
 
  • #3
192
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ok so how can i solve it?
and is told that the Standard deviation are 2
so for example if i know the Variance and it 4 so to find the Standard deviation i just need to do sqrt4.
and in this case i know the Standard deviation so to find the Variance i need to do 2^2 instead of sqrt4. no?

thank you.
 
  • #4
192
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ok so how can i solve it?
and is told that the Standard deviation are 2
so for example if i know the Variance and it 4 so to find the Standard deviation i just need to do sqrt4.
and in this case i know the Standard deviation so to find the Variance i need to do 2^2 instead of sqrt4. no?

thank you.
 
  • #5
vela
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You're given stdev(X)=2 tons. You can't just square it to find the variance of Y, which is a different random variable.
 
  • #6
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so can you give me any way to solve it or give me direction ?

thanks
 
  • #7
vela
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Look up in your textbook how the variances of X and Y are related.
 
  • #8
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well is will be correct to say:
if i use the formula var(aX+b)=a^2var(X) and then i will put numbers and get this:
9*4=36 and this is the Variance Income from the Tomato in this Sampled?

thanks.
 
  • #9
HallsofIvy
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Yes,that is correct. Are you interested in how that formula is derived?

For the variable x, the mean is given by
[tex]\mu_x= \frac{\sum x_i}{n}[/tex]
while, for the variable y, it is
[tex]\mu_y= \frac{\sum y_i}{n}[/tex].

If y= ax+ b, that is the same as
[tex]\mu_y= \frac{\sum (ax_i+ b)}{n}= \frac{a\sum x_i+ \sum b}{n}= a\frac{\sum x_i}{n}+ \frac{nb}{n}[/itex][itex]= a\mu_x+ b[/tex].

For the variable x, the variance is given by
[tex]v_x= \frac{\sum (x_i- \mu_x)^2}{n}[/tex]
while, for the variable y, it is
[tex]v_y= \frac{\sum (y_i- \mu_y)^2}{n}[/tex].

Again, if y= ax+ b, that is
[tex]v_y= \frac{\sum (ax_i+ b- (a\mu_x+ b))^2}{n}=[/itex][itex] \frac{\sum{(ax_i- a\mu_x)^2}{n}[/tex]
[tex]= \frac{a^2(x_i- \mu_x)^2}{n}= a^2\frac{(x_i- \mu_x)^2}{n}= a^2 v_x[/tex].
 
  • #10
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WOW.
thanks for show all this way.
 

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