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- NT #3 For each of the following, answer whether the distribution of X is necessarily normally distributed (YES) or not (NO), and briefly explain why. a) X = the sample mean age for random samples of size n = 50 from the population of New Yorkers of non-working age (defined as below 18 or above 64). b) X = the sample mean age for random samples of size n = 10 from the population of New Yorkers of non-working age (defined as below 18 or above 64). c) X = the sample mean age for random samples of size n = 10 from a population of individuals whose ages are known to be normally distributed.if (xoy) - X 2 2 · 10-10 3 0.15 0.20 0.30 5 0·10 0·15 a. Determine the marginal distribution g(x), x=2, 4 b. Determine the marginal distribution h(y), y = 1,3,5 c. Determine the cumulative distribution punction F(x) 4What is the following: 1. Sum of X 2. Sum of Y 3. Sum of X2
- (c) A certain form of 'triangular' distribution has c.d.f.add to F(x) = 1-(1-x)², 0Below are some frequency distribution data that were collected from a recent experiment that looks at musicians and their ability to improvise. Let’s say for the sake of this example that these are continuous data. X is the number of years playing piano, and f is the frequency reported. X f7 66 55 54 53 12 21 00 2 a. Compute the median number of years that participants reported playing the piano without using a formula.The production of jute goods (in tons) in different days of first and second half of the year are shown below: Class interval of production No. 2-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 of 12 48 70 35 15 days in the first half of the year No. of 5 38 80 50 7. days in the second half of the year In which part of the year the production level is homogeneous?Not sure how to answer questions C through E. Suppose that X has a (continuous) uniform distribution between 10 and 20 (a) Compute E (X). (b) Compute Var (X). (c) Compute P (X < 12). (d) Compute P (X > 12). (e) Compute P (X < 8 or X > 22).The profits of a mobile company are normally distributed with Mean of R.O (180) and standard deviatic of R.O (8). a. Find the probability that a randomly selected mobile has a profit greaterthan R.O ( 190). b. Any mobile phone which profit is greater than R.O (190) is defined as expensive. Find the probability that a randomly selected mobile has aprofit greaterthan R.O ( (200) given that it is expensive. Half of expensivemobile phones have aprofit greaterthan R.O h. Find the value of h. C.A biologist is monitoring several small groups of elk. Each group is made of one or two "resident" males, however during mating season "bachelor" males will challenge the resident males of the heard. The biologist records the following information about the encounter. Identify each of the variables below as Categorical, Quantitative Discrete, Quantitative Continuous, or Identifier. Who won the challenge - the bachelor or the resident How long the challenge lasts How many cows (females) are in the group Estimation of the general health of the group, on a scale of 1 (poor) to 5 (robust) Designation/name of the group1. We are working in a bakery. 15.62% of all bakery customers will buy a cookie, and you may assume that customers can't buy more than one cookie at a time. Visualize the following distributions in R. Be sure to write out the pmf and submit screenshots of your code and pictures of the plots/graphs. (a) Let X indicate whether the next customer buys a cookie. 1 (b) Let X be the number of customers, out of the next 38, who buys a cookie. (c) The bakery likes all cookies to be fresh, so they don't make that many at a time: they only bake batches of 12. Let X be the number of customers until they sell all of the first batch of cookies (d) Let X be the number of chocolate chip cookies which are brought to you if you ask the server to randomly select 4 cookies from a platter containing 5 chocolate chip, 3 oatmeal, and 7 peanut butter.3. Suppose that X has an exponential distribution with a mean of 10. Determine the following: (a) P(X 15) (c) Compare the results in parts (a) and (b) and comment on the role of memoryless property.If the range of Xis the set {0,1,2,3,4,5,6,7,8} and P(X= x) is defined in the following table: 1 2 3 4 5 6 7 8 P(X = x) 0.07961 0.2660 0.1992 0.0665 0.01960 0.0665 0.08022 0.08944 0.1330 determine the mean and variance of the random variable. Round your answers to two decimal places. (a) Mean = i (b) Variance = iSEE MORE QUESTIONS