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1. Suppose we play a game where we start with c dollars. On each play of the game you either double or halve your money, with equal probability. What is your expected fortune after n trials?
2. Show that V(X) = 0 if and only if there is a constant c such that P (X = c)= 1.
3. Let X1,..., Xn ∼ Uniform(0, 1) and let Yn = max{X1,..., Xn}. Find E(Yn).
4. A particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump the probability is p that the particle will jump one unit to the left and the probability is 1-p that the particle will jump one unit to the right. Let Xn be the position of the particle after n units. Find E(Xn) and V(Xn). (This is known as a random walk.)
A group of children can be classified according to eye color (blue, brown, green), gender (male, female), and hobby (collecting stamps, collecting baseball cards, collecting shells, collecting stickers).
Mean waiting time was 15 minutes and that the standard deviation was 4 minutes. The 95% confidence interval for the population mean of waiting times is?
Children per family for certain community from census data. Recognize random variable of interest, find out whether is a discrete or continuos, and write its possible values.
a sample of 27 of 172 funded projects revealed that 11 were valued at 17300 each and 16 were valued at 20220 each. from
in random samples of 900 men and 400 women it is found the 99 men and 36 women suffer from kidney stones. is there
When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100
a clinical trial tests a method designed to increase the probability of conceiving a girl. in the study 562 babies were
Let A ⊆ {1, 2, 3, . . . , 25} where |A| = 9. For any subset of A let sB denote the sum of the elements in B. Prove that there are distinct subsets C, D of A such that |C| = |D| = 5 and sC = sD.
Determining probability when guessing answers. Test comprise of multiple- choice questions each having 4 possible answers (a, b, c, d) one of which is right. Suppose that you guess answers to six such questions.
Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?
you roll two fair dice a green one and a red one.a what is the probability of getting a sum of 6? enter your answer as
1. What is the difference between a histogram and a bar chart? For what type of data would each be appropriate? 2. The following U.S. market shares for 2007 retail car sales have been reported. Source: World Almanac and Book of Facts 2009, p. 122.
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