DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
16th Edition
ISBN: 9781323235911
Author: BITTINGER
Publisher: Pearson Custom Publishing
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Chapter J, Problem 13DE
To determine
To calculate: The value of
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Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6.
a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…
4. Consider Chebychev's equation
(1 - x²)y" - xy + λy = 0
with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant.
(a) Show that Chebychev's equation can be expressed in Sturm-Liouville form
d
· (py') + qy + Ary = 0,
dx
y(1) = 0, y(-1) = 0,
where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2
(b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the
functional A[y], where
A[y]
=
I[y]
J[y]'
and I[y] and [y] are defined by
-
I [y] = √, (my² — qy²) dx
and
J[y] = [[", ry² dx.
Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1.
1
(c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable
4
trial functions for estimating the smallest eigenvalue. Show that the value of A[y]
for these trial functions is
4k2
A[y] =
=
4k - 1'
and use this to estimate the smallest eigenvalue \1.
Hint:
L₁ x²(1 − ²)³¹ dr =
1
(1 - x²)³ dx
(ẞ > 0).
2ẞ
2. If loga b + log, a = √√29, find all possible values of loga blog, a
Chapter J Solutions
DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
Ch. J - Find the square roots.
1.
Ch. J - Prob. 2DECh. J - Prob. 3DECh. J - Prob. 4DECh. J - Prob. 5DECh. J - Prob. 6DECh. J - Prob. 7DECh. J - Prob. 8DECh. J - Prob. 9DECh. J - Prob. 10DE
Ch. J - Prob. 11DECh. J - Prob. 12DECh. J - Prob. 13DECh. J - Prob. 14DECh. J - Prob. 15DECh. J - Prob. 16DECh. J - Prob. 17DECh. J - Prob. 18DECh. J - Prob. 19DECh. J - Prob. 20DECh. J - Prob. 21DECh. J - Prob. 22DECh. J - Prob. 23DECh. J - Prob. 24DECh. J - Prob. 25DECh. J - Prob. 26DECh. J - Prob. 27DECh. J - Prob. 28DECh. J - Prob. 29DECh. J - Prob. 30DECh. J - Prob. 31DECh. J - Prob. 32DECh. J - Prob. 33DECh. J - Prob. 34DECh. J - Prob. 35DECh. J - Prob. 36DECh. J - Prob. 37DECh. J - Prob. 38DECh. J - Prob. 39DECh. J - Prob. 40DECh. J - Prob. 41DECh. J - Prob. 42DECh. J - Prob. 43DECh. J - Prob. 44DECh. J - Prob. 45DECh. J - Prob. 46DECh. J - Prob. 47DECh. J - Prob. 48DECh. J - Prob. 49DECh. J - Prob. 50DECh. J - Prob. 51DECh. J - Prob. 52DECh. J - Prob. 53DECh. J - Prob. 54DECh. J - Prob. 55DECh. J - Prob. 56DECh. J - Prob. 57DECh. J - Prob. 58DECh. J - Prob. 59DECh. J - Prob. 60DECh. J - Prob. 61DECh. J - Prob. 62DECh. J - Prob. 63DECh. J - Prob. 64DECh. J - Prob. 65DECh. J - Prob. 66DECh. J - Prob. 1ESCh. J - Prob. 2ESCh. J - Prob. 3ESCh. J - Prob. 4ESCh. J - Prob. 5ESCh. J - Prob. 6ESCh. J - Prob. 7ESCh. J - Prob. 8ESCh. J - Prob. 9ESCh. J - Prob. 10ESCh. J - Prob. 11ESCh. J - Prob. 12ESCh. J - Prob. 13ESCh. J - Prob. 14ESCh. J - Prob. 15ESCh. J - Prob. 16ESCh. J - Prob. 17ESCh. J - Prob. 18ESCh. J - Prob. 19ESCh. J - Prob. 20ESCh. J - Prob. 21ESCh. J - Prob. 22ESCh. J - Prob. 23ESCh. J - Prob. 24ESCh. J - Prob. 25ESCh. J - Prob. 26ESCh. J - Prob. 27ESCh. J - Prob. 28ESCh. J - Prob. 29ESCh. J - Prob. 30ESCh. J - Prob. 31ESCh. J - Prob. 32ESCh. J - Prob. 33ESCh. J - Prob. 34ESCh. J - Prob. 35ESCh. J - Prob. 36ESCh. J - Prob. 37ESCh. J - Prob. 38ESCh. J - Prob. 39ESCh. J - Prob. 40ESCh. J - Prob. 41ESCh. J - Prob. 42ESCh. J - Prob. 43ESCh. J - Prob. 44ESCh. J - Prob. 45ESCh. J - Prob. 46ESCh. J - Prob. 47ESCh. J - Prob. 48ESCh. J - Prob. 49ESCh. J - Prob. 50ESCh. J - Prob. 51ESCh. J - Prob. 52ESCh. J - Prob. 53ESCh. J - Prob. 54ESCh. J - Prob. 55ESCh. J - Prob. 56ESCh. J - e
Rewrite without rational exponents, and...Ch. J - Prob. 58ESCh. J - Prob. 59ESCh. J - Prob. 60ESCh. J - Prob. 61ESCh. J - Prob. 62ESCh. J - Prob. 63ESCh. J - Prob. 64ESCh. J - Prob. 65ESCh. J - Prob. 66ESCh. J - Prob. 67ESCh. J - Prob. 68ESCh. J - Prob. 69ESCh. J - Prob. 70ESCh. J - Prob. 71ESCh. J - Prob. 72ESCh. J - Prob. 73ESCh. J - Prob. 74ESCh. J - Prob. 75ESCh. J - Prob. 76ESCh. J - Prob. 77ESCh. J - Prob. 78ESCh. J - Prob. 79ESCh. J - Prob. 80ESCh. J - Prob. 81ESCh. J - Prob. 82ESCh. J - Prob. 83ESCh. J - Prob. 84ESCh. J - Prob. 85ESCh. J - Prob. 86ESCh. J - Prob. 87ESCh. J - Prob. 88ESCh. J - Prob. 89ESCh. J - Prob. 90ESCh. J - Prob. 91ESCh. J - Prob. 92ESCh. J - Prob. 93ESCh. J - Prob. 94ES
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