Many people believe that the daily charge of a price of a company's stock on the stock market is a random variable with mean 0 and variance {see attachment}. That is, if Yn represents the price of the stock on the n-th day, then (see equation in attachment( where X1,X2,..., are independent and identically distributed random variables with mean 0 and variance {see attachment}.

Suppose that the stock's price today is 100. If the variance =1, what can you say about that probability that the stock's price will exceed 105 after 10 days, without using the Central Limit Theorem?

Suppose that a probability distribution has a mean 20 and standard deviation 3. The Chebychev inequality states that the probability that an outcome lies between 16 and 24 is:
a. less than 7/16
b. at least 7/16
c. at most 1/4
d. at least 1/4
e. none of the above

These questions are a part of a Operations Research class with a section on Reliability Theory.
(See attached file for full problem description with proper symbols and equations)
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Question
Let N be a non-negative, integer-valued random variable, Show that
P{N > 0} >= (E[N])2

If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality
Given percentage (87%), does the empirical rule apply?
What does the Empirical Rule s

1. The ______________can be used to differentiate the "vital few" causes of quality problems from the "trivial many" causes of quality problems.
A) histogram
B) scatter plot
C) Pareto chart
D) box plot
2. Which display is most likely to reveal association?
A) Dot plot.
B) Scatter plot.
C) Histogram.
D)

Please help with the following problem regarding probability. Provide calculations and explanations.
1. The probability of contracting the kissing disease is .23 when one is exposed to a certain provocative environment. Sixty people are so exposed. What is the probability that no more than 10 are infected with this dreaded d

The Tchebychev inequality can also be stated in the following way:
For any random variable x with mean equal to μ and variance equal to Δ². The minimum probability of X belong to the interval X?[ μ-k, μ+k] is at least:
P( | X- μ|

1. Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?
Write an inequality to be solved with the answer. In your inequality, use both the multiplication and addition properties of inequalities.
2. How do you know if a value is

1. Explain how synthetic division may be used to find the factors/zeros of a polynomial function. Give an example of how this is accomplished.
Use synthetic division to find the function value.
1) f(x) = 2x4 + 4x3 + 2x2 + 3x + 8; find f(-2).
Write the quadratic function in the form y = a(x - h)2 + k.
2) y = x2 - 2x - 9

In the judicial case of United States vs. City of Chicago, discrimination was charged in a qualifying exam for the position of Fire Captain. In the table below Group A is a minority group and Group B is a Majority Group.
Passed Failed
Group A 10 14
Group B 417 145
A) If one of the test subjects is randomly selected,