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Question: Consider the following Table:
Y 0 1 2 3
P(Y) 0.10 0.30 0.40
a) Complete the Table with the probability of P(X = 3).
b) Calculate the mean, variance and standard deviation of Y.
c) Suppose now we have a new random variable X = 2 + 3Y. Construct a Table with the probability distribution of X for each value of Y and X.
d) Calculate the mean, variance and standard deviation of X.
e) Use the properties of the expected value and variance to obtain the expected value of X, E(X), and the variance of X, V(X). Compare your answers.
Use normal approximation to determine probability that x = 2. Illustrate all work.
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What is the difference between a null hypothesis and an alternate hypothesis? Explain what is meant by the critical value of a statistical value.
Also, the sample data appear to have a bell-shaped distribution. Construct the 95% confidence interval for the mean time spent on paperwork by all managers.
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you have purchased five shares of stock in diversified machine tools which has a mean value of 25 and a standard
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You take a random sample around town and calculate a p-value for your hypothesis test of 0.0913. What is the appropriate conclusion? Conclude at the 5% level of significance.
You may use the manual method of calculation, or show how MegaStat (or other software) is used to analyze the data. Be sure to discuss the interpretation of results.
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