Answer:
A = choosing a red marble
B = choosing a green marble
Probability of A happening = P(A) = 5/(3+5+4) = 5/12
Probability of B happening = P(B) = 4/(3+5+4) = 4/12
Probability of either happening = P(A) + P(B) = 5/12 + 4/12 = 7/12
The key word in their question is red OR green and that is why we add the two probabilities. If they ask the probability of them both happening (if they said red AND green), you would multiply P(A)*P(B).
<u>The three important tools of Federal Reserve's monetary policies are as follows:</u>
- open market operations
- the discount rate
- reserve requirements.
<u>Step-by-step explanation:</u>
The monetary policies of the United States's central bank, Federal Reserve are the acts of the entity to influence money and raise the country's economy. These policies also helps in looking over the aspects of how the money and credits draw affects on credit rates and the overall performance of the U.S. Economy.
The three prime tools of the Federal reserve's monetary policies are the Open Market Operations, Discount Rates and the Reserve Requirements.
<u>Open Market operations</u>
This involves in purchase and selling process of government securities. The primary dealer with which the Reserve deals compete on the basis of prices and thus the dealer gets decided with whom the reserve deal for the day.
<u>Discount Rates</u>
This is the discount rate charged to depository institutions for short term loans by the Federal Reserve.
<u>Reserve Requirements</u>
This is the money or deposit amount the Reserve Bank must sustain in its vault or depository.
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
