Hi there what you need is lagrange multipliers for constrained minimisation. It works like this,
V(X)=α2σ2X¯1+β2\sigma2X¯2
Now we want to minimise this subject to α+β=1 or α−β−1=0.
We proceed by writing a function of alpha and beta (the paramters you want to change to minimse the variance of X, but we also introduce another parameter that multiplies the sum to zero constraint. Thus we want to minimise
f(α,β,λ)=α2σ2X¯1+β2σ2X¯2+λ(\alpha−β−1).
We partially differentiate this function w.r.t each parameter and set each partial derivative equal to zero. This gives;
∂f∂α=2ασ2X¯1+λ=0
∂f∂β=2βσ2X¯2+λ=0
∂f∂λ=α+β−1=0
Setting the first two partial derivatives equal we get
α=βσ2X¯2σ2X¯1
Substituting 1−α into this expression for beta and re-arranging for alpha gives the result for alpha. Repeating the same steps but isolating beta gives the beta result.
Lagrange multipliers and constrained minimisation crop up often in stats problems. I hope this helps!And gosh that was a lot to type!xd
to get his wage for the next day, you would do 18x1.2, which equals 21.6, so he would now be making $21.6 per hour.
Answer: Option B) 7,214
Step-by-step explanation:
The value of the digit 2 in 5,426 is 20.
-In 2,843, the place value of 2 is 2000
- In 7,214, the place value of 2 is 200
- In 43,928, the place value of 2 is 20
- In 67,452, the place value of 2 is 2
So, since he place value of 2 in 7,214 is 200; and since 200 is ten times more than 20 (i.e 20 x 10 = 200)
Thus, the answer is 7214