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Let {Xn}n∈N0 be a simple symmetric random walk ( ).
What is the probability that Xn will visit all the points in the set {1,2,3,4} at least once during the time-interval n ∈ {0,...,10}?
(Note: write your answer as a sum of binomial coefficients; you don't have to evaluate it any further.)
Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2): Is it a vector space, if not demonstrate which axioms fail to hold.
If you have 280 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
a shipment of 150 television sets contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive (a) no defective units, (b) all defective units and, (c) at least one good unit.
At a selling price of $ 65 , a lamp company breaks even on total sales of $ 4550 . If the company's overhead is $ 420 , find the marginal production cost per lamp and find the profit on sales of 154 lamps.
how many seconds after the rock is thrown will it reach maximum height, and what is that height in meters? how many seconds after the rock is thrown will it reach the ground?
In a survey of 200 employees of a company regarding their 401K investments, the following data were obtained:
How fast is the spotlight moving along the wall containing the gate (in feet per minute) when it hits Bob if Bob is 1200 feet from the gate along the side of the rectangle containing the only gate?
What are the mean value and standard deviation of the resistance distribution?
The base of an aquarium with volume V = 220 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
A plane flying horizontally at an altitude of 1 mi and a speed of 440 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station.
the runners are running on circular tracks of which has a circumference of 1320 feet. the tracks are 100 feet apart and and the runners start opposite each other and move at the same constant rate of 880 ft/min. how fast are the runners separating..
Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n
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