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1. Consider the model Y t = β 0 + β 1 X t + ε t , where t = 1,..., n. If the errors ε t are not correlated, then the OLS estimates of β 0 and β
A spring has a natural length of 20 Centimeter. A 40 N force is needed to stretch and hold the spring to a length of 30 Centimeter. How much work is completed in stretching the spr
Write a script to determine the volume of a pyramid, which is 1/3 * base * height, where the base is length * width. On time the user to enter values for the length, width, and th
Recognizes the absolute extrema & relative extrema for the following function. f ( x ) = x 2 on [-1, 2] Solution: As this function is simpl
Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:
sin(xy)+x=5y Find the derivative.
1+1=?
Fundamental Theorem of Calculus, Part I If f(x) is continuous on [a,b] so, g(x) = a ∫ x f(t) dt is continuous on [a,b] and this is differentiable on (a, b) and as,
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
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