MAD 4401 ASSIGNMENT-Work the following problems. This is for extra credit

| August 31, 2017

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MAD 4401 ASSIGNMENT
JAMES KEESLING

Work the following problems. This is for extra credit. The problems also help prepare
for Test 2. Use the class periods on April 8 and 10 to work together on the problems. Each
person should turn in the assignment individually on Monday 4/13/15.
Problem 1. There are three urns, I, II, and III. Each urn has white balls and black balls.
Urn I has 3W and 4B, Urn II has 7W and 1B. Urn III has 2W and 6B. An urn is chosen at
random and a ball is chosen at random out of the urn. What is the probability that Urn
II was chosen given that the ball was black?
Problem 2. Suppose that a certain bowler will produce a strike with probability .85,
a spare with probability .10, and have an open frame with probability .05. Using the
bowling program to estimate the probability that such a bowler will bowl 200 or greater
in a game.
Problem 3. Consider the differential equation dx = t2 · x with initial condition x(0) = 2.
dt
Solve this differential equation numerically on [0, 1] using the Euler and Runge Kutta
methods with h = 1/10 and n = 10. Give the estimated values of the points to eight digits.
Problem 4. Determine the Taylor expansion for the solution of the differential equation
dx
2
1
dt = t · x with x(0) = 1. Determine the expansion to the t 0 term, x(t) ≈ a0 + a1 · t + a2 ·
2 + a · t3 + a · t4 + a · t5 + a · t6 + a · t7 + a · t8 + a · t9 + a · t10 .
t
3
4
5
6
7
8
9
10
Problem 5. Derive the steady-state probabilities for a single server queue M/M/∞/FIFO
with service rate σ and arrival rate α.

1

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