Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
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Chebyshev’s Theorem and The Empirical Rule Suppose we ask 1000 people what their age is. If this is a representative sample then there will be very few people of 1-2 years old just as there will not be many 95 year olds. Most will have an age somewhere in their 30’s or 40’s. A list of the number of people of a certain age may look like this: |Age |Number of people | |0 |1 | |1 |2 | |2 |3
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Newton ’s laws of motion Newton ’s laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces. They have been expressed in several different ways over nearly three centuries and can be summarized as follows: 1. First law: The velocity of a body (a state of rest or of uniform motion in a straight line) remains constant unless the body is compelled to change that state
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Welcome to Tv6’s special today‚ I am ‚ and I will be your host‚ we will be reviewing 3 special segments that all involve Newton’s 3 laws. Let’s go take a look at the first one. As you just saw in this Polo segment‚ Newton’s first law is one of the reason this game exists‚ if you hit the ball with the polo sick the reason for the ball to continue in motion is because of Newton’s First Law‚ “An object in motion will remain in motion unless an external force acts upon it.” But the reasons behind the
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Greek mathematician and philosopher. Pythagoras was responsible for important developments in the history of mathematics‚ astronomy‚ and the theory of music. The thing that Pythagoras is probably the most famous for is the Pythagorean Theorem. The Pythagorean Theorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides. This means that if one makes a square (with all sides equal in
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Algebra II‚ 7th period 11th March 2013 The Life and Works of Sir Isaac Newton Sir Isaac Newton‚ (1642-1727)‚ mathematician and physicist‚ was one of the greatest scientific minds of all time. Sir Isaac Newton was born at on January 4th (December 25th old calendar) at Woolsthorpe‚ a farmstead‚ in Lincolnshire. Woolsthorpe is the place where he worked on his theory of light and optics. This is also believed to be the site where Newton observed an apple fall from a tree‚ inspiring him to make his law
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In the late 1960’s and early ’70’s posters of the Black Panther Party’s co-founder‚ Huey P. Newton were taped and plastered on walls of college dorm rooms nation-wide. Wearing a black beret and a leather jacket‚ sitting on a wicker chair‚ a spear in one hand and a rifle in the other‚ the poster portrayed Huey Newton as a symbol of his generation’s anger and courage. He was a symbol of anger and courage in the face of racism and the class in which blacks were placed. His intellect and leadership abilities
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Case Study Part 1- Specifications Table (MS Word) Go to Course Content > Project Instructions > Case Study Instructions Director Request to see the instructions and grading criteria for the case study prior to looking at this part of the case study. Part 1: For the case study outlines in the Instructions topic‚ create MS Word tables that identify and contain the hardware and software requirements to meet the director’s requirements. The MS Word document in its final form will include
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Newton’s I‚ II‚ & III Law Newton’s three laws of motion explain everything that happens to objects in Earth. Anything from kicking a ball to a human being walking is explained by Newton’s three laws of motion. They explain something different of the motion of an object‚ put together they explain everything. In order they are; Newton’s First Law: The law of inertia; Newton’s Second Law: The law with the concept of acceleration; Newton’s Third Law: The Law of Action & Reaction. Newton’s
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Geometry Definitions‚ Postulates and Theorems Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement
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