(i) Annual claim frequency for an individual policyholder has mean 2 and variance c (ii) The prior distribution for 2 is uniform on the interval [0.5, 1.5]. (iii) The prior distribution for o? is exponential with mean 1.25. A policyholder is selected at random and observed to have no claims in Year 1. Using Bühlmann credibility, estimate the number of claims in Year 2 for the selected policyholder. (A) 0.56 (B) 0.65 (C) 0.71 (D) 0.83 (E) 0.94
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- The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios†. 24 16 22 14 12 13 17 22 15 19 23 13 11 18 The sample mean is x≈ 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is μ = 19. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and σ = 4.1. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use ? = 0.01. What is the level of significance? What is the value of the sample test statistic? (Round your answer to two decimal places.) Find (or estimate) the P-value. (Round your answer to four decimal places.)The monthly stock return of IBM is normally distributed with mean 0.08 and standard deviation 0.04. (i)What is (?)? What is ??(?)? What is ?(?)? (ii)What is the probability that the stock return is lower than 0.08? (iii)What is the probability that the stock return is between 0.04 and 0.07? (b)What five steps do we need to follow when conducting hypothesis testing? (c)Based on a random sample of 16 customers, the mean amount spent on fast food by an individual per year equals $240. At the significance level ?? = 0.05, Helen would like to test if the population mean amount spent on fast food per year equals $311, as reported by an industry report. It is known that the amount spent on fast food per year is normally distributed with a standard deviation $140plovabllity distribution. i Find the expected value and the standard deviation for the distribution in (i) above. 9. A team of 3 players is to be chosen from 4 boys and 5 girls. Find the: (i) probability distribution for the number of girls in the team. (ii) expected value and the standard deviation for the distribution in (i) above. 6.
- The distribution of the time it takes for different people to solve a certain crossword puzzle is skewed to the right,with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is(a) Normally distributed, with mean 30 and standard deviation 15.(b) skewed to the right, with mean 30 and standard deviation 15.(c) Normally distributed, with mean 0 and standard deviation 1.(d) skewed to the right, with mean 0 and standard deviation 1.(e) skewed to the right, but the mean and standard deviation cannot be determined without more information.Calculate the geometric mean return of the following returns Date Return 11/01/2018 5.96% 11/14/2018 6.05% 12/01/2018 0.29% 12/14/2018 1.18% NOTE: Enter the PERCENTAGE number rounding to two decimals. If your decimal answer is 0.034576, your answer must be 3.46. DO NOT USE the % sign Calculate the variance for the returns below Date Return 11/01/2018 0.6% 11/14/2018 6.7% 12/01/2018 -4.31% 12/14/2018 2.55% NOTE: Enter the DECIMAL number rounding to four decimals. If your decimal answer is 0.034576, your answer must be 0.0346. DO NOT USE the % sign5. Suppose the time spent by a randomly selected student at a campus computer laboratory has a gamma distribution with mean 20 min and variance 80 min². (a) What are the values of a and B? (b) What is the probability that a student spends between 20 and 40 min at the laboratory? (c) Only 1% of students will spend more than how many minutes at the laboratory?
- The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 15% of UGPAS? (b) Between what two values does the middle 50% of the UGPAS lie? (a) The minimum UGPA that would still place a student in the top 15% of UGPAs is (Round to two decimal places as needed.). on the low end and on the high end. (b) The middle 50% of UGPAs lies between (Round to two decimal places as needed.) hp WE H 3.42 G=0.17 2.84 3.42 Grade point average Time Remaining: 00:34:06 Submit test Q QBlack Water CO(BWO) TATA Steel (TATA) 1.Estimate the average daily return of each fund using the arithmetic average method. (EXCEL) Below are the historical closing prices for the two funds above. 2. Calculate the standard deviation of each fund (EXCEL) Date BWO TATA 3. Calculate the correlation between the two funds 10/20/2016 113.3374 113.6971 4. Calculate the covariance between the two funds using a) Excel function, Covariance.S 10/21/2016 113.7611 113.6408 and b) using formula (Correlation multiplied by standard deviations of both funds. 10/24/2016 115.1283 114.3635 10/25/2016 114.7624 113.5094 10/26/2016 113.9825 112.383 10/27/2016 113.4626 111.0971 10/28/2016 112.7501 110.7873 10/31/2016 112.6442 111.2285 11/1/2016 111.7969 109.8675 11/2/2016 110.9014 108.4689 11/3/2016 109.8134 107.9433 11/4/2016 109.4282 108.6379 11/7/2016 112.0279 111.2942 11/8/2016 112.7597 111.5852 11/9/2016 113.2797 115.0206 11/10/2016 111.4502 116.8603 11/11/2016 111.4984 119.5448The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 5% of UGPAS? (b) Between what two values does the middle 50% of the UGPAs lie? (a) The minimum UGPA that would still place a student in the top 5% of UGPAS is (Round to two decimal places as needed.) H=3.30 a=0.18 3.30 Grade point average O Q