Suppose X has the following distribution 1 2|n||n| + 1) P{X = n} = = for n = ±1, ±2,.... (a) What are all medians of X? (b) What is the mean of X? Hint: To get started, compute the following two sums: ΣnP{X = n} and Σ-nP{X = n}. n=1 n=1
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It is given that the PDF of X is:
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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.Question 3 According to the historical data, 72.9% of the 20-year-olds live until 65 years old. A random sample of size 70 was obtained. Let be the proportion of the sample that live until 65 years old. ) to describe the probability distribution of pand 1. Use the Central Limit Theorem (Select an answer Select an answer np>10 and n(1-p)>10 n(1-p)10 np10 state its parameters and op: (Round the answers to 4 decimal places) p~ Select an answer Select an answer N X² unknown F T B (H₂ 3 op= 2. Find the probability that more than 85% of the sample live until 65 years old. (Round the answer to 4 decimal places)The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20–39 in the United States. Apply the cnormal to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. Р(X > 122) — .356 Incorrect
- Answe d and eLet X be the number of scoring chances that result in goals for a football team during n scoring chances. During many games, the team scores on 20% of the chances. a) Explain why it might be reasonable (at least as an approximation) to assume that X is binomially distributed in this situation. Do this by going through each of the points that must be met for us to use the binomial distribution, assess whether it is reasonable for them to be met here and specify any additional assumptions we need to make.Eighteen individuals are scheduled to take a driving test at a particularDMV office on a certain day, eight of whom will be taking the test for thefirst time. Suppose that six of these individuals are randomly assigned toa particular examiner, and let Xbe the number among the six who aretaking the test for the first time. a. What kind of a distribution does Xhave (name and values of allparameters)?b. Compute P(X = 2), P(X ≤ 2), and P(X≥2).c. Calculate the mean value and standard deviation of X.
- A function randomly generates 4-digit decimal numbers in the range of 0000 to 9999 (all have the same chance) what is the probability that there will be a repeated digit? E.g; 1891 (1 is repeated), or 2272 (2 is repeated 3x)this helps... but the question is asking what is the expected times we would flip a head. My thinking is that we use the same approach as above but replace the [1..9] with 0 for (1/2)^10 and 1 for (1/2) .. (1/2)^9. I'm also not sure how to handle if the 10th flip is a head? Thanks!2A. X is normally distributed with a mean of 8 and standard devaition is of 0.5. Determine P(8.44(less than or equal to)X)
