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Let B(t) be a Brownian motion. Show that the following processes are Brownian motions on [0, T ].
1. X(t) = -B(t).
2. X(t) = B(T - t) - B(T), where T < +∞.
3. X(t) = cB(t/c2), where T ≤ +∞.
4. X(t) = tB(1/t), t > 0, and X(0) = 0.
Exercise 3.20: Let Sn = S0 + (sigma from n to i=1 of ξi) be a Random Walk, with P(ξ1 = 1) = p, P(ξ1 = -1) = 1 - p. Show that for any λ, eγSn-λn is a martingale for the appropriate value of γ.
An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it..
A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a 75 degree room at time t = 0 minutes.
The figure below show a telephone wire hanging between two poles at x = - b and x = b. It takes the shape of a catenary with equation y = c + a Find the length of the wire.
Rate related problems and Determine the general expression for the car's acceleration at any time t, and show that car is decelerating 2(2/3) seconds after starting from rest.
This problem is basically from Mathematics and it is about finding the log for the given number.
a bacteria culture grows according to the formula n t -4t2 40t 25 where n is the number of bacteria after t minutes
jill and jamahl are comparing their sprcial numbers. jills number has a prime factorization with six prime numbers.
The following data sets shows the ages of the first seven presidents (president washington through president jackson) and the seven most recent presidents including president obama. Age is given at time of inauguration.
In your own words in a complete sentences, address the following question: For any quadratic function on any interval, at what point in that interval is the tangent line parallel to the secant line through the endpoints of the graph
1. Plot the complex number.z= 4 + 5i 2. Find the absolute value of the complex number.z= 14i 3. Write the complex number in polar form. Express the argument in degrees.z= 5i
A hot metal bar is submerged in a large reservoir of water whose temperature is 60 degrees F. The temperature of the bar 20s after submersion is 100 degrees F. After 1 minute, the temp has cooled to 80 degrees F.
A is the event that a prime number comes up, B is the event that a number divisible by three comes up, C is the event that a perfect square number comes up. Find the sample space S, find complementary events, mutually exclusive events.
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