What is P(X =2)?
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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.
A: The answer provided below has been developed in a clear step by step manner.
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Q: Indicate that R and R2 may be covered by countably many open balls.
A: To show that ℝ and ℝ2 covered by countably many open balls.
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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls
A: As per the question we have to prove that both ℝ and ℝ2 may be covered by countably many open balls.
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- In Major league Baseball (MLB), the American League baseball teams play their home games with the designated hitter (DH). This rule gives the team the ability to have a batter take the place in the batting order of the pitcher. The league believes that by replacing the pitcher (usually a poor hitter), there will be more hits, more runs and therefore, more interest from fans. (David “Big Papi” Ortiz of the Red Sox is an example of a modern day DH). Below are the average runs scored in the American League and National League home games during the past 14 seasons. American League 11.4 9.9 10.5 9.7 10.4 9.1 10.3 9 10.2 9.0 10 8.9 9.9 8.8 National League 10.5 9.5 10.3 9.4 10 9.1 10 9 9.7 9 9.7 8.9 9.6 8.9 a) Is there evidence to suggest that the DH does lead to increased scoring in the American League? (Name hypothesis, Check conditions, .....etc)Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than 15 from w.Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert. Show that the number of ways to seat the 3 married couples attending a concert is equal to 72 if and only if members of the same sex are all seated next to each other in the 6 row seats?
- A building contains 1000 lightbulbs. Each bulb lasts at most five months. The company maintaining the building is trying to decide whether it is worthwhile to practice a “group replacement” policy. Under a group replacement policy, all bulbs are replaced every T months (where T is to be determined). Also, bulbs are replaced when they burn out. Assume that it costs $0.05 to replace each bulb during a group replacement and $0.20 to replace each burned-out bulb if it is replaced individually. How would you use simulation to determine whether a group replacement policy is worthwhile?The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used. Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are.A type of small snail is very widespread in Japan, and colonies of the snails that are genetically similar have been found very far apart. Scientists wondered how the snails could travel such long distances. A recent study provides. the answer. Biologist Shinichiro Wada fed 174 live snails to birds and found that 26 of the snails were excreted live out the other end. The snails appar- ently are able to seal their shells shut to keep the digestive fluids from getting in. Estimate the standard error (use the standard deviation in the picture for the standard error) question 2: Use the standard error from part (b) to find a 95% confidence interval for the proportion of all snails of this type to live after being eaten by a bird. Write both ends of your interval as percents,
- Students at certain university have to pass of one these three courses (MAT102, STA105, and PHY110). The pass rates for the courses MAT 102, STA105, and PHY110 are 0.54, 0.79, and 0.86, respectively. Suppose that 30 candidates take the MAT102 course, 25 take the STA105 course and 20 take the PHY110 coruse. A student takes one of these courses and passes. What are the probabilities that she took MAT102, STA105 or PHY110? Hint: Denote by Q the event a student to pass their course. Now denote by R1, R2 and R3 the events to take courses MAT102, STA105, and PHY110. The pass reates then represent the conditional probabilites: P(Q| R1), P(Q| R2) and P(Q| R3). The number of students taking the courses can be used to estimate the probabilities for R1, R2 and R3. For example, since there are total of 30 + 25 + 20 = 75 students that take the courses, for R1 we have: P(R1) = 30/75 = 2/5 What you are asked is: given that a student passes (event Q) estimate the probabilities that she took MAT102…Suppose we have an urn with a total of 10 balls where 5 balls are marked with number "1" and 5 balls are marked with number "0”. Suppose we draw two balls without replacement from the urn. Let the number on the first ball be X1 and the number on the second ball be X2. Find P(X1 >=X2). (Note: Justify all your steps.)Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to afree package of garden seeds. At the Healthy Crunch home office, they use the weightof incoming mail to determine how many of their employees are to be assigned tocollecting coupons and mailing out seed packages on a given day. (Healthy Crunch hasa policy of answering all its mail on the day it is received.)Let x = weight of incoming mail and y = number of employees required to process themail in one working day. A random sample of 8 days gave the following data:x (lb) 11 20 16 6 12 18 23 25y (Number of employees) 6 10 9 5 8 14 13 16a.) Draw a scatter diagram for the datab.) Find the equation of the least-squares line. Plot the line on the scatter diagram forpart (a).c.) Find the sample correlation coefficient r and the coefficient of determination ??.d.) If Healthy Crunch receives 15 pounds of mail, how many employees should beassigned mail duty that day? Show work
- A researcher wants to determine the specificity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the results below from a study: Out of a total of 18 women with breast cancer, 12 screened positive and 6 screened negative on the mammogram. Out of a total of 82 women without breast cancer, 5 screened positive and 77 screened negative on the mammogram. Calculate and interpret the specificity of mammograms for detecting breast cancer.The king is planning a new rectangular courtyard in his palace. It will be laid out using square tiles. He has chosen some very pretty, but very inexpensive, tiles. However, his adviser has informed him that some of the tiles will have to be a more expensive type. This is because visiting dignitaries will always walk along a certain diagonal, from one corner of the courtyard to the opposite corner, so the tiles along this diagonal will get lots of wear and tear. Every tile that contains a segment of the diagonal must thus be an extra-strength, more expensive tile. If a tile touches the diagonal only at a corner, it can be a regular tile. The diagram shows what the situation would look like if the king made a 4-by-6 courtyard. In this case, 8 tiles (shaded darker than the rest) include some portion of the diagonal, so these would need to be the more expensive kind. 1. The king wants to know how many of these special tiles to order. At the moment, he is planning a 63-by-90 tile…Show that both ℝ and ℝ2 may be covered by countably many open balls.