From a given triangle of unit area, we choose two points independently with uniform distribution. The straight line connecting these points divides the triangle, with probability one, into a triangle...
From a given triangle of unit area, we choose two points independently with uniform distribution. The straight line connecting these points divides the triangle, with probability one, into a triangle and a quadrilateral. Calculate the expected values of the areas of these two regions.
Homework Answers
Answer:
Expected value for the area of triangle is 4/9
Expected value for the area of quadrilateral is 5/9.
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From a given triangle of unit area, we choose two points independently with uniform distribution. The straight line connecting these points divides the triangle, with probability one, into a triangle...
Choose two numbers X and Y independently at random from the unit interval [0,1] with the...
Choose two numbers X and Y independently at random from the unit interval [0,1] with the uniform density. The probability that X^2+Y^2>0.81 is ?
4. (3 pts) Two points are picked independently and uniformly from the region inside a unit circle...
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4. In triangle ABC we are given the following: a = 16 cm, b = 20...
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Problem 5 . This question considers uniform random points on the unit disc x2+92 〈 1...
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Electric potential for a continuous charge distribution: Let's consider a line of charge, of length L...
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4. (3 pts) Two points are picked independently and uniformly from the region inside a unit circle. Let R1 and R2 be the distances of these points from the center of the circle. Find P(RIR2/2). Hint: To find the probability distribution oR it is easier to consider the c.d.f.
4. (3 pts) Two points are picked independently and uniformly from the region inside a unit circle. Let R1 and R2 be the distances of these points from the center of...
4. In triangle ABC we are given the following: a = 16 cm, b = 20 cm, ZC = 70°. (i) Use the law of cosines to calculate the value of c to the nearest hundredth of a unit of length. (ii) Use the law of sines to calculate the measure of ZA to the nearest degree. (iii) Find the measure of ZB. (iv) Determine whether the given data produce one triangle, two triangles, or no triangle at all. (v)...
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1. (2 points) What are the two requirements for a probability distribution? 2. (8 points) Suppose Lonzo has basketball practice three days a week. Seventy percent of the time, he attends all three practices. Ten percent of the time, he attends two practices. Three percent of the time he only attend one practice. a. Let X- b. X takes on what values? Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table). The table should...
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