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In a classical ruin problem with two gamblers, the initial capital of one of the gamblers, Alice, is $90 and the combined initial capital (CIC) is $200. In each trial of the game, an unbiased coin is tossed - Alice wins when the coin shows heads.
a) What is the expected duration of the game?
b) Given the same CIC, how much more money should Alice have ititially so as to maximize the expected duration of the game?
Sketch density curves that might explain distributions with fallowing shapes: symmetric, but with two peaks( i.e., two strong clusters of observations)
Iit is known that signal change in this brain area is normally distributed with mean of 35 and standard deviation of 10. By using .01 level, what must researcher conclude?
One of the most famous probability calculations is called the "birthday problem". In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people
a. What is the probability of a type I error? b. Give the formula for the test statistic.
In a simple linear regression analysis of 18 data points the following ANOVA table was found.
To findout 95 percent with confidence interval for the mean amount a citation. Police Chief Aaron Ard of River City reports 500 traffic citations were issued last month.
If all samples of size 64 are drawn, mean of sample according to Central Limit Theorem is 100.
Explain clearly, in your own words, what is a Type I error in this context.
Test whether the mean rate is less than 6%. Use P-value approach.
To determine whether two categorical variables are independent, one should use the:
A two-way ANOVA model was used to analyze an experiment with two levels of one factor, three levels of a second factor, and 6 observations per treatment combination.
Exam is given to 20 randomly chosen students and their average length of t time needed to finish exam was 54 minutes with standard deviation of 5.99 minutes. Test instructor's claim at the 0.05 level of significance.
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