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Question: An unenlightened gambler
(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets heavily on black at the next spin. Asked why, he explains that black is "due by the law of averages." Explain to the gambler what is wrong with this reasoning.
(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
A random sample of 100 highway runs of the new model yields a sample mean of 32 miles per gallon. Give a 95% confidence interval for the population average miles-per-gallon highway rating.
a certain brand of fluorescent light tube was advertised as having an effective life span before burning out of 4000
Write such an equation in terms of the relevant variables above for the beginning of each of the years to obtain the five functional constraints for this problem.
Test at the alpha = 0.10 level, whether the manufacturer's claim is true.
If the first head occurs on the first toss, you win $1. If the first head occurs on toss 2 or on toss 3 you win $2 or $3, respectively. If no heads appear, you lose $1 (that is, win -$1). Find the joint probability function for Y1 and Y2.
Between 1872 and 2000, stock prices rose in 74% of the years (M. Hulbert, The Stock Market Must Rise in 2002? Think Again, The New York Times, December 6, 2001)
Past studies indicate that only 85% of booked passengers show up for their flight. Find the probability that if the airline books 150 persons for a 140-seat plane, not enough seats will be available.
Let (X1, Y1) and (X2, Y2) be independent and identically distributed continuous bivariate random variables with joint probability density function
What is the expected value and variance of the number of deliveries in a 700-letter group?
A chi-square test of the statistical significance of the relationship has a p-value of .19. Is this evidence that there is a relationship? What is the justification for this conclusion?
A random sample of 77 eighth grade students' scores on a nation mathematics assessment test has a mean score of 278 with a standard deviation of 31.
Compute the expected return of stock a and compute the standard deviation - compute the expected return ?B. Compute the standard deviation ?C. Presuming the stock returns are normally distributed, what do these results indicate?
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