Calculate Variance of Tomato Crop Income: Steps & Answers

[omni]

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.

 

[vela]

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.

 

[omni]

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.

 

[omni]

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.

 

[vela]

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.

 

[omni]

so can you give me any way to solve it or give me direction ?

thanks

 

[vela]

Look up in your textbook how the variances of X and Y are related.

 

[omni]

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.

 

[HallsofIvy]

Yes,that is correct. Are you interested in how that formula is derived?

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

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]$= a\mu_x+ b$[/tex][itex].<br /> <br /> For the variable x, the variance is given by <br /> $$v_x= \frac{\sum (x_i- \mu_x)^2}{n}$$<br /> while, for the variable y, it is <br /> $$v_y= \frac{\sum (y_i- \mu_y)^2}{n}$$.<br /> <br /> Again, if y= ax+ b, that is <br /> $$v_y= \frac{\sum (ax_i+ b- (a\mu_x+ b))^2}{n}=$$[/itex][tex]$\frac{\sum{(ax_i- a\mu_x)^2}{n}$[/tex][itex] $$= \frac{a^2(x_i- \mu_x)^2}{n}= a^2\frac{(x_i- \mu_x)^2}{n}= a^2 v_x$$.[/itex]

 

[omni]

WOW.
thanks for show all this way.