Let the interval [-r,r] be the base of a semicircle. If a point is selected at random from this interval, assign a probability to the event that the length of the perpendicular segment from the point to the semicircle is less than r/2. Answer this by using Pythagorean theorem and explain all of the steps well and clearly.
Let the interval [-r,r] be the base of a semicircle. If a point is selected at...
Let the interval [-r,r] be the base of a semicircle. If a point is selected at random from this interval, assign a probability to the event that the length of the perpendicular segment from the point to the semicircle is less than r/2. Answer this by using Pythagorean theorem and explain all of the steps well and clearly.
With diagram -16 Let the interval |-r.r]be the base of a semicircle. Ifa point isselected at random from this interval, assign a probability to the event that the length of the perpendicular segment from this point to the semicircle is less than r/2
are even, r even. A 1.1-14·Let the interval [-r,r] be the base of a semicircle. ne of the f a pot is selected at random from this interval, assign abilty of a probability to the event that the length of the perpen- e slot into dicular segment from the point to the semicircle is less than r/2. 1.1-15. Let S = A1 U A2 U U Am, where events (a) If P(A1) P(A2)P(A), show that P(Ai - (b) If A...
Let C be the semicircle of radius r > 0 with center at (0, 0) and lying above the x-axis. For each x in [−r, r], let L(x) be the length of the line from (x, 0) to the semicircle C and perpendicular to the x-axis. What is the probability that L(x) is less than r/2?
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4 3 marks (b) Suppose X, and X2 are two iid normal N(μ, σ2) variables. Define Are random variables V and W independent? Mathematically justify your answer. 3 marks] (c) Let C denote the unit circle...
1. (a) A point is selected at random on the unit interval, dividing it into two pieces with total length 1. Find the probability that the ratio of the length of the shorter piece to the length of the longer piece is less than 1/4. 3 marks (b) Suppose X1 and X2 are two iid normal N(μ, σ*) variables. Define Are random variables V and W independent? Mathematically justify your answer 3 marks (c) Let C denote the unit circle...
4. A flexible plastic rod can be charged and bent into a semicircle. Using the method of "breaking the object" into many point charges and then integrating the electric field from those charges, derive an equation for the electric field components at the center of the semicircle for a rod of length L, bent into a semicircle of radius R, with charge Q. Hints: Use the angle for your position of each "point charge". The length of a small segment...
Submit Test This Question: 2 pts 11 of 16 (11 complete) This Test: 39 pts possible Explain how you would find the distance XY across the lake shown below, and then find XY. 50 m Y 100 m 200 m Which of the following explains how to find the distance XY? O A. Draw a perpendicular segment from Y to the segment representing 200 m. Then draw the segment XY. A right triangle is formed with side lengths 100 m...
Let R be the region shown above bounded by the curve C = C1[C2. C1 is a semicircle with center at the origin O and radius 9 5 . C2 is part of an ellipse with center at (4; 0), horizontal semi-axis a = 5 and vertical semi-axis b = 3. Thanks a lot for your help:) 1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
Suppose that a point X is selected at random from the interval (0,1). After the value X = x has been selected, a point Y is then chosen at random from the interval (0,x^2). a) Indicate the region R on the xy-plane of possible values of the random vector (X,Y). b) Find the marginal pdf f2(y) of Y.