What is the expectation (to 2 decimal places) of Y? ELY
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- In 1938, a physicist named Frank Benford discovered that the number 1 appears in the first digit of random data more often than the number 2, the number 2 more often than the number 3 and so on. In general, the probability of occurrence of the first digit of a number can be written in the form of a probability function x + 1 P(X = x) = log. X a. Prove it P(X = x) = log ) untuk x = 1,2,3,4...,9 x+1 X x = 1,2,3,4..., 9 is a probability mass function 2 b. Find the cumulative distribution function of X!a Deline the following terms as used in survival analysis (eft rensoring (i) Informative censoring ThaVbeg cendng n hich ue (b) Let the event of interest be contracting lung cancer. The lung cancer hazard rate for an d - Cato what 3nd male Imoker is gven ty (e)=0.027 +0.00025(-40),xz 40 Assuming that a 40-year old nale smoker is still alive at his age S0, tetermine the pritability that he survives to age 50 without contracting lung cancer?6c.) Draw the graphs. Round your final answers up to 6 decimal places, if applicable. Give the correct units.
- The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = k·P(X = k) 7 (or more) P(X=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 k 1 2 3 5 6 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %.where is the 500 coming from when finding the expected frequency?Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
- B. Find the following probabilities using the t-table if X~t20 a. P(T > 0.860) b. P(T < - 1.325) C. Find k such that P(k< T< 2.947) = 0.845 when T~t15A coin which has probability 0.83 of coming up Heads is tossed three times. Let Y be the number of Tails observed. Find E(Y2), giving your answer correct to two decimal places. Answer:
