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1. Let X be a random variable with µ = E(X) and σ2 = V (X). Define X∗ = (X -µ)/σ. The random variable X∗ is called the standardized random variable associated with X. Show that this standardized random variable has expected value 0 and variance 1.
2. Peter and Paul play Heads or Tails. Let Wn be Peter's winnings after n matches. Show that E(Wn) = 0 and V (Wn) = n.
3. Find the expected value and the variance for the number of boys and the number of girls in a royal family that has children until there is a boy or until there are three children, whichever comes first.
With a mean of 33 oz. and a standard deviation of 0.7 oz. 95% of packets actually contain more than x oz. of soap powder. What is x?
Assuming that the data may be viewed as a random sample from a normal population, construct a 95% con?dence interval for the actual average diameter of bearings made by this process and interpret.
Scatter plot, Correlation coefficient and Regression equation - Do a complete regression analysis by performing the steps below
Compute the value of the test statistic (to 2 decimals).
Develop null and alternative hypotheses to help the bank determine which option would provide the best incentive to consumers.
a random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. assuming that the
Test hypothesis that annual incomes of corporate trainers in areas of more than 500,000 are considerably more than those in areas of less than 100,000. Make use of the 5% level of risk.
Each of 2 cabinets identical in appearance has 2 drawers. Cabinet A contains a silver coin in each drawer, and cabinet B contains a silver coin in one of its drawers and a gold coin in the other. A cabinet is randomly selected, one of its drawers ..
A supermarket advertises that the waiting time spend by customers waiting in line at the cash register is uniform between 0 and 6 minutes.
a survey of statistics students includes information on their age college major expected salary after graduation and
When 40 people used the Weight Watcher diet for one year, their mean weight loss was 3.0lb and the standard deviation was 4.9 lb (based on data from "Comparison of the Atkins, Ornish, Weight Watcher, and Zone Diets for Weight Loss and Heart Diseas..
suppose that the average number of airline crashes in a country is 1.9 per month.a what is the probability that there
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