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

August 31, 2017

estion
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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