Determine the distribution of Xn for the following Let X1, X2.....X15 be a random sample from Bin (10, ²)
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- 12 q5Craps: In the game of craps, a pair of dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 12. The probability 1 that you win is and if you win, your profit is $30. If you lose, you lose $1. 36 Part: 0/2 Part 1 of 2 (a) What is the expected value of your profit? Round the answer to two decimal places. 1 The expected value of profit is Skip Part 75 Check dollars. MacBook Air U X Ś Save For Later Submit Assignment 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 8 I 000 8: 0 3Let n be a random sample from the exp(0) Show that X is a sufficient statistic for
- only need d,e,fAssume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
- 3. Let Y,,. , Y, be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?The average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 13 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 13, 13, 11, 13, 13, 13, 13, 10, 12, 13, 13, 10, 13 What can be concluded at the the αα = 0.05 level of significance level of significance? The null and alternative hypotheses would be: H0 = (p,u) (<,>,=,not equal) to _____ H1 = (p,u) (<,>,=,not equal) to _____ The test statistic (t,z) = ___ The p-value = _____ Thus, the final conclusion is that ... The data suggest that the population mean wait time for men who wear a tie is not significantly more than 12 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 12. The data suggest the population mean is not significantly more than 12…24. Show that the mean x of a random sample of size n from the distribution : 1 f (x, €) =e, 0 0 x/e e? is the M.L.E. of 0 with variance