Distribution with probability density function
Suppose that the we have the following data which comes from a distribution with probability density function
f(x,θ) = θx^(θ-1) 0 < x < 1
Show how you could generate observations from this distribution if is known.
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Graph the empirical cumulative distribution for the following 12 measurements: 9,10,6,7,9,7,9,6,8,5,10,12
Give an example of a question that can be answered using tools of descriptive statistics. (C)Give an example of a question that can be answered using the tools of inferential statistics.
Show that the ratio of two independent standard normal random variables has the t1 distribution.
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Let F hat denote the empirical distribution function based on a random sample X1,....Xn with common cdf F.= Show that E[ F hat (x)] = F(x) and Var[ F hat (x)] = F(x)(1 - F(x))=n.
In the casino dice game of craps, the shooter rolls two (fair) dice. The shooter a) wins on the first roll if the sum of the dice is 7 or 11 and b) loses on the first roll if the dice total 2, 3, or 12. Calculate the probability of winning on the
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Five cards are independently and randomly picked from a standard 52 card deck and each card is recorded in sequence. Each card that is picked is then put back in the deck, so it is possible to record the same card more than once.
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