Numerade

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At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon. a. In words, dene the Random Variable X. b. List the values that X may take on. c. Give the distribution of X. d. How many are expected to not use the foil as their main weapon? e. Find the probability that six do not use the foil as their main weapon. f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.

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A school newspaper reporter decides torandomly survey 12 students to see if they will attend Tet festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. a. In words, dene the Random Variable X. b. List the values that X may take on. c. Give the distribution of X. d. How many of the 12 students do we expect to attend the festivities? e. Find the probability that at most 4 students will attend. f. Find the probability that more than 2 students will attend.

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f(x) = frac{5-x}{10}, quad x = 1, 2, 3, 4.

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Let X be a continuous random variable with the probality density function f( x ) = C x, 5 ? x ? 11, zero otherwise. a. Find the value of C that would make f( x ) a valid probability density function. b. Find the probability P( X > 7 ). c. Find the mean of the probability distribution of X. d. Find the median of the probability distribution of X.

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In a casino game chuck-a-luck, three unbiased six-sided dice are rolled.One possible bet is $1 on fives, and the payoff is equal to $1 for each five on that roll. In addition, the dollar bet is returned if at least one five is rolled. The dollar that was bet is lost only if no fives are rolled. Let X denote the payoff for this game. Then X can equal – 1, 1, 2, or 3. a) Determine the p.m.f. f( x ). b) Calculate µ and ?2.

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Alex makes mistakes in class according to Poisson process with an average rate of 1.2 mistakes per class. a. What is the probability that Alex makes at least 3 mistakes during one class? b. What is the probability that Alex makes exactly 10 mistakes during two weeks of classes (that is, during 6 classes, since Alex teaches a MWF lecture)?

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An advertising company has 12 men and 8 women. Suppose the company needs to select a team of 5 members to work on a commercial for the new hybrid car, Hyper Geo Metro 2015. a. If the members of the team are selected at random, what is the probability that 3 men and 2 women will be selected? b. What is the probability that men will constitute a majority in the team?

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Alex takes a multiple choice quiz in his Anthropology 100 class.The quiz has 10 questions, each has 4 possible answers, only one of which is correct. Alex did not study for the quiz, so he guesses independently on every question. What is the probability that Alex answers exactly 2 questions correctly?

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f(x) = c(x+1)^2, x = 0, 1, 2, 3.

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egin{tabular}{c|c} ( x ) & ( f(x) ) \ hline 0 & 0.1 \ 1 & 0.1 \ 2 & 0.3 \ 3 & 0.3 \ 4 & 0.2 end{tabular}

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Ünsal T.