Think of this situation as a system of equations.
let y be the price of hotdogs
let x be the price of hamburgers
5y + 2x = 8
2y + 5x = 9.50
now use your solution method of choice
substitution, elimination, matrices, etc
Answer:
a) b) the standard deviation and the mean is affected by the conversion factor as well
c) the mean is displaced by b units
Step-by-step explanation:
for a new variable
Y=a*X , where a= constant (conversion factor= 1 kg/2.2 pounds)
then
p(y)= p(a*X) = p(X)
a) mean =μ=E(Y)= ∑ a*X*p(y) = a ∑ X*p(x) = a* E(X)
mean =μ=a*μₓ
b) σ² = ∑ (Y-μ)²* p(y) = ∑ (a*X-a μₓ)²* p(y) = a²*∑ (X-μₓ)²* p(x) = a²*σₓ²
then
standard deviation = σ= √σ²=√(a²*σₓ²) = a*σₓ
standard deviation = σ= a*σₓ
then the standard deviation and the mean is affected by the conversion factor as well
c) nevertheless for a displacement b
Y₂=X + b (b= constant= 50 gr)
p(Y₂)= p(X + b) = p(X)
then
mean =μ=∑ (X-b)*p(y)=∑ X*p(x)- b ∑ p(x) = E(X) -
mean =μ=μₓ - b
then the mean is displaced by b units
This is an example of empirical probability, although it gives the same ratio as a theoretical probability, because we based the result on our experiment
You didn't show us much of the page with the question on it,
so we can't be sure of exactly what you're working on in math.
If you're working with things like squares and rectangles, then
'L' and 'W' are often used to represent the Length and Width of
shapes drawn on paper, or even Length and Width of 3D objects
like blocks or boxes.
