8007 試験問題を無料オンラインアクセス

The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

• A.x = -1, y = 0
• B.x = 0, y = 20
• C.None of the above
• D.x = 5, y = 0

What can be said about observations of random variables that are i.i.d. a normally distributed?

• A.The estimated mean divided by the estimated standard deviation has a t-distribution
• B.The estimated mean divided by the estimated standard deviation has a Chi2-distribution
• C.The estimated mean divided by the estimated variance has a t-distribution
• D.The estimated mean divided by the estimated variance has a Chi2-distribution

Which statement regarding the matrix below is true?

• A.It is negative definite
• B.It is positive definite
• C.It is not positive definite
• D.It is positive semi-definite

I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

• A.2.50%
• B.5%
• C.-5%
• D.-2.50%

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

• A.-x/(x+y) - y/(x+y)
• B.ln(x+y) x + ln(x+y) y
• C.1 / (x+y)
• D.(x + y) / (x+y)