Based on a detailed medical examination, a doctor declares that the odds of a patient developing a certain disease are 2. From this it follows that the probability the patient will develop the disease is: 1/4 O 1/2 3/4 1/3 O 2/3
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A: The answer is given below step.
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- A fair coin is flipped 3 times. What is the probability that the flips follow the exact sequence below? Flip One: Heads Flip Two: Heads Flip Three: Tails ⅛ ⅜ ⅓ ⅔ ½The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses fewer than 400 minutes? 0 0.023 0.159 0.977Using the standard normal distribution, what is the probability that z>1.3936 ? O 0.0409 0.9183 1.8366 0.1634 0.0817
- The Frequentist approach says that given 10 coin flips you should get exactly 5 heads and 5 tails. Question 15 options: True False The Frequentist approach says that, in the long run, if we flip a coin a large number of times, we would expect an approximate 50-50 split of heads and tails. Question 16 options: True False Consider multiple trials of flipping a fair coin. As the number of trials decreases, the closer we get to an equal split of heads and tails. Question 17 options: True False The following would represent probability from the Frequentist approach: After rolling a six-sided die 300 times, we would expect to roll a 2 or a 3 about 33% of the time. Question 18 options: True FalseA coin is flipped 8 times in a row (assume all outcomes are equally likely). For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. Q1.1 What is the probability that it lands on heads exactly four times?Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.
- There are 7 balls hidden in a box (3 blue and 4 green). If you first select a green ball and do not replace in the box, what is the probability that the second ball you select from the box will also be green? [Your answer can be written either as a fraction or decimal]You are given an exam with questions numbered 1, 2, 3, . . . , n. Each question i is worth pi points and has a frustration score fi . You must answer the questions in order, but you may choose to skip some questions. The reason you might choose to do this is that even though you can solve any individual question i and obtain the ???? points, some questions are so frustrating that after solving them you will be unable to solve any of the following fi questions. Suppose that you are given the pi and fi values for all the questions as input. Devise an efficient algorithm you can for choosing a set of questions to answer that maximizes your total points, and compute its asymptotic worst case running time as a function of n.Probability and Statistics I have in my pocket ten coins. Nine of them are ordinary coins with equal chances of coming up head and tail when tossed and the tenth has two heads. If I toss the coin and it comes up heads, what is the probability that it is the coin with two heads?
- Dynamic Programming: Two coins X and YFlip coin X: gain 1 point for the head, and lose 1 point for the tailFlip coin Y: gain 3 points for the head, lose 3 points for the tail. After n round, if the final score is positive, you win. Otherwise, you lose. The score does not matter. Pr(s) be the probability of winning; r is the round; s is the score.P0(s) = 1 for s >= 1; P0(s) = 0 if s <= 0. a. Explain why P1(s) = 0 when s <= -3; P1(s) = 0.5 when -2 <= s <= 1; P1(s) = 1 for s >= 2. b. Explain why you must select X if s is 2 or 3, and you must select Y if s is −2 or −1. b. Determine P2(s) for each possible value of s and explain. (each probability will be one of 0, ¼, 1/2, ¾, 1) c. Fine a recurrence relation for Pr(s) with form Pr(s) = max[(?+?)/2, (?+?)/2]. Explain. d. Use Dynamic Programming to compute probability P100(0) (win the game if it has 100 rounds).The ACT is a standardized test used by college admissions offices as a factor in whether an applicant is or is not admitted to their college. Since so many students take this test each year, the distribution of results are typically approximately normal. The table below shows the mean and standard deviation for each section of within the ACT for all test takers in the years 2015, 2016, and 2017. Section Mean Standard Deviation English 20.3 6.8 Math 20.7 5.4 Reading 21.4 6.5 Science 20.9 5.5 STEM 21.0 5.2 What are the z-score and the percentile rank of a student who scored 22 in the Math section of the ACT? z = percentileComputer Science Investing in stocks is a way to create assets that are supposed to provide financial security over time. In solving this problem, we assume that an investor buys several shares of stock at a certain price. These shares are going to be sold later on for a different price. Obviously, if the selling price is higher than the acquisition price, the investor makes a profit, registering capital gain. If the shares are sold at a lower price, the investor has a loss, which marks a negative capital gain. This whole process is done over a period of time, and you are required to create a scenario for buying and selling shares. The assumption is that the investor sells shares in the order in which they were purchased. The goal is to calculate the capital gain over time. Suppose that you buy n shares of stock or mutual fund for d dollars each. Later, you sell some of these shares. If the sale price exceeds the purchase price, you have made a profit—a capital gain. On the other…