Answer:
See the proof below.
Step-by-step explanation:
For this case we just need to apply properties of expected value. We know that the estimator is given by:
And we want to proof that 
So we can begin with this:
And we can distribute the expected value into the temrs like this:
And we know that the expected value for the estimator of the variance s is 
, or in other way 
so if we apply this property here we have:
And we know that 
so using this we can take common factor like this:
And then we see that the pooled variance is an unbiased estimator for the population variance when we have two population with the same variance.
I don't think you copied it correctly, but I'll assume that you did.
y = 4x³ - 2x² + 5('x' to the -3.7 power) - 6
"y-prime" (the first derivative) = 12x² - 4x - 18.5('x' to the -4.7 power)
Answer:
270
Step-by-step explanation:
Given that :
Ratio = 14:8:5
Houses : flats : bungalow
Number of bungalow = 50
Sum of ratio = (14 + 8 + 5) = 27
Let total number of households = x
Bungalow = 5/27 * x
5/27 * x = 50
5x / 27 = 50
5x = 50 * 27
5x = 1350
x = 1350 / 5
x = 270
Number of places to live = 270
