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Exercise # 1: Collect and Comment on the variability of thr...

Exercise # 1: Collect and Comment on the variability of three recent data sets describing similar processes (could be prices of three items over the last month, demographic information related to 3 countries over last year, etc.). Exercise # 2: Plot the probability mass function (PMF) and the c...

4) Consider an urn containing 4 black balls and 8 white ball...

4) Consider an urn containing 4 black balls and 8 white balls, and consider randomly and independently drawing, with replacement, a ball from the urn 9 times. (Note: When the draws are done with replacement, each time a ball is randomly selected, there are always 4 black balls and 8 white balls to...

Question 2 Tail bounds based on moments In this problem we...

Question 2 Tail bounds based on moments In this problem we will develop tail inequalities when we know some moments of a random variable. We will use the notation 14k = E[X*] for the k-th moment. Recall that Var[X] = 12 - 117. (a) Here we develop a one-sided Chebyshev's inequality. Show that fo...

3) Suppose that balls will be sequentially removed (one at a...

3) Suppose that balls will be sequentially removed (one at a time) from an urn initially containing 4 amber and 4 blue balls, until the only balls left in the urn are all the same color. Letting X be the number of balls in the urn when all of the balls in the urn are the same color, give the cdf of ...

7 (C) One of your students was reading about permutations an...

7 (C) One of your students was reading about permutations and came across the formula: nPr = n. She is now confused since she learned that the formula was nPr - n(n - 1) (n - 2) (n - r + 1). How can you help her resolve her confusion? 9 (C) (a) You give your students the following problem: &am...

In Tim Hostons Roll up the Rim, 1 out of 6 cups is a winnin...

In Tim Hostons Roll up the Rim, 1 out of 6 cups is a winning cup, you buy 2 or 3 cups every day. (Decision of choosing 2 or 3 cups is independent) P(2 cups) = 0.8 P(3 cups) - 0.2 (a) Find P["Winning 1 in 1 day"] (b) Find PC"O wins in 2 days"]

Let A and B be two events in a sample space S such that P(A)...

Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A n B) = 0.18. Find the probabilities below. (a) P(A)B) (b) P(B)A) If A and B are independent events, P(A) = 0.15, and P(B) = 0.55, find the probabilities below. (Enter your answers to four decimal places.) (a)...

Two cards are selected at random without replacement from a ...

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to three decimal places.) A pair is not drawn. Five balls are selected at random without replacement from an urn containing four white ba...

Problem 2: In a one minute interval, the number of requests ...

Problem 2: In a one minute interval, the number of requests for access to a web-based game is a Poisson random variable with a mean of 20. (a) Find the probability that more than 25 requests are received in the one minute interval by applying the central limit theorem. (Hint: apply the de Moivre-La...

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