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Question: Consider the following gambling game for two players, Black and white. Black puts black balls and white puts w white balls in a box. Black and white take turns at drawing at random from the box, with replacement between draws until either Black wins by drawing a black ball or white wins by drawing a white ball. Suppose black gets to draw first.
a) Calculate P(Black wins) and P(White wins) in terms of P = b/(b + w).
b) What value of p would make the game fair (equal chances of winning)?
c) Is the game ever fair?
d) What is the least total number of balls in the game, (b + w), such that neither player has more than a 51% chance of winning?
An opinion poll in California uses random digit dialing to choose telephone numbers at random. Numbers are selected separately within each California area code.
The ages of the cadets in the sample will form a normal distribution.
you flip a coin 60 times. you get heads 45 times and tails 15 times. calculate a 95 confidence interval for the true
Delayed jobs normally results in lost business, which estimated to be C2 per job per week.Determine the optimum production rate?
(a) What is the average cost per hour if Mary is hired? If Alice is hired? (b) Find C if the average cost per hour is the same for Mary and Alice.
Suppose {a_n} (n=1 to N) and {b_n} (n=1 to N) are two finite sequences of complex numbers. Let B_k = sum b_n (sum n=1 to k) denote the partial sum of the series sum (b_n) with the convention B_0=0.
A random variable X has a uniform distribution over the interval (-a/2, a/2) for some positive constant a:- Find the coefficient of skewness for X ; - Find the coefficient of kurtosis for X ;
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Suppose we had used 10,000 in places of 1,000 in the simulations. What would the final graph have looked like.
First, write out the expres- sion for the exact determination of the cut-off point, and secondly, use the CLT for its numerical determination.
The 154-day weights (in pounds) of 16 randomly selected Rambouillet lambs on a farm in Nebraska were recorded. The data are given in the following table.
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