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Let {Xn}n∈N0 be a symmetric simple random walk. For n ∈ N the average of the random walk on the interval [0,n] is defined by
Is {An}n∈N0 a simple random walk (not necessarily symmetric)? Explain carefully using the definition.
Compute the covariance Cov(Xk,Xl) = E[(Xk - E[Xk])(Xl - E[Xl])], for k ≤ l ∈ N
Compute the variance of An, for n ∈ N.
The size, P, of a certain insect population at time t (in days) obeys the equation P = 500e0.02t. What is the initial population of the insect population
A box with a square base has length plus girth of 114 in. (Girth is the distance "around" the box.) What are the two possible lengths of the box, if its volume is 2000 in3?
Mathis, Inc. is a designer and manufacturer of women's clothing and specializes in high-end women's winter fashions. Normandale, a retailer, sells high-end products in malls throughout the country. With Mathis's high costs, Normandale is unable to..
A bomber flying at a height of 30,000 ft and 540 mph spots its target at an angle of depression of 10 degrees. At what angle of depression should the bomber release its bomb in order to hit the target?
the area of a rectangle is 100 square inches. the perimeter of the rectangle is 40 inches. a second rectangle has the
Find the constants. Find the center of mass of the solid bounded below by the cone z2 = x2 + y2 and above by the sphere x2 + y2 + z2 = 2az and whose density is kz.
Read the Nature article, Sustainable Trophy Hunting of African Lions and discuss any challenges in the analysis. Can you think of another ways to do the regression analysis?
How many samples contain at least 1 rotten apple?
A mortgage at 9% interest compounded monthly with a monthly payment of $1125 has an unpaid balance of $10,000 after 350 months. Find the unpaid balance after 351 months.
1. A. express the quadratic function in standard form B. find its vertex and its x and y intercepts C. sketch its graph
A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?
a container in the shape of an inverted right circular coner has a radius of 8 inches at the top and a height of 10 inches. At the instant when teh water in the container is 8 inches deep the surface level is falling at the rate of -1.3in/s. FInd ..
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