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The following problem develop the concept of determining the probability distribution of random variable and its mean and variance.
A fair coin is tossed three times. Describe the sample space Ω.
Let X be random variable that denotes the number of heads on the first toss. Describe the probability frequencydistribution of X. Find the mean E(X) and variance Var(X).
Let Y be another random variable that counts the total number of heads. Describe the probability frequency distributionof Y , and evaluate E(Y) and Var(Y ).
Describe the frequency distribution of the ordered pair Z = (X, Y ). Then evaluate E(Z) and Var(Z).
Describe the frequency distribution of the product W = XY . Then evaluate E(W) and Var(W).
Is the z value positive or negative? Explain why it should be positive or negative.
What reasons for complaints do you think the hotel should focus on if it wants to reduce the number of complaints? Describe.
The population of lengths of aluminium coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.20 inches. A sample of four metal sheets is randomly selected from a batch. What is the possibility that t..
Find the probability that a random sample of 4 male Siberian tigers will have a sample mean weight more than 450 lb.
Using data provided, test if there is a difference between means at alpha =.05.
The data consists of random sample of 30 households from the 2007 American Community Survey. Construct a frequency distribution and a histogram for each data set.
The following data represent glucose blood levels(mg/100ml) after a 12 hour fast for random sample of 70 women: Employ 6 classes and make a frequency distribution table.
When the Sharpe Ratio for the market portfolio is 0.5, what risk-free rate Rf is the market anticipate? Draw on a diagram for the Capital Market Line derived from the above data. Make sure to clarify the intercept and the slope.
The average time a subscriber spends reading the Wall Street Journal is 49 minutes. Assume that the standard deviation is 16 minutes and the time are normally distributed .
Obtain a test statistic and p -value assuming equal variances. Interpret these results.
a) Set up the null and alternative hypotheses, and perform the hypothesis test. b) Based on these results, does the diet appear to be effective? Does the diet appear to have practical significance?
Computing the mean and standard errors of sampling distribution - Using the central limit theorem, find the means and standard errors of sampling distributions
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