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![2. Let Z₁, Z₂ be a random sample from a standard normal distribution, and X₁, X₂ a random sample from
a Normal (1,1) distribution. Answer the following questions
a. What is the distribution of X + Z?
b. What is the distribution of [(x₁-x₂)²+(Z₁-Z₂)²+(Z₁ +Z₂)²] ?
2
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- 7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).24. How does the t distribution differ from the Z distribution? a. It has a smaller standard deviation and hence thinner tails than the Z distribution. b. It has a larger standard deviation and hence thicker tails than the Z distribution. c. The t and Z distributions are no different.3. For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n= 65 and p = 0.7 a. Normal approximation is not suitable. b. Normal approximation is suitable.
- Q2Please assist with all questions and add R script as well.6. a normal distribution has a mean of 65 and an SD of 20. For each of the following samples, compute the z score for the sample mean and determine whether the mean is typical or extreme. (calculate a Z STATISTIC) I a. M=74 for a sample of 4 scores B.M=74 for a sample of 25 scores 8: F2 *3 # E D 80 F3 C 54 4 R F a V % 5 F5 T G 6 B MacBook Air Y H 87 & FEB 27 N U N 00 8 J DII M ( 9
- Q6Use the data in the Excel workbook, on the worksheet labeled "Sample," for this question. The first column is just an observation index labeled i to name each observation. The observations are a simple random sample with replacement from a much larger population. The second column contains specific values y of a random variable Y found in some sampled population. The population standard deviation is not known to you, but it is known that Y has a Normal distribution in the sampled population. Compute the lower bound of an 85% confidence interval for the population mean of the random variable Y. i y 1 37 2 40 3 31 4 27 5 23 6 33 7 29 8 26 9 39 10 28 11 34 12 39 13 31 14 34 15 39 16 33 17 31 18 42For the questions below, please show the derivation of the distributions step by step. (a) Suppose that the random variables X₁,..., X, form a random sample from a standard normal distribution. Let (b) Y = (X₁ + X₂ + X₂ + X₁)² + (X₂ + X6 + X₁ + X)². Obtain the c value so that the random variable cY has a x² distribution. Suppose that X₁,..., X, are independent and identically distributed random variables from a standard normal distribution. Obtain the value of d so that the random variable has at distribution. d(x₁ - + X₂ + X₂) (X₂²+X₂²+X₂² X,²)/² (c) If S and S are the variance for the sample of independent random variables with size n₁ = 6 and n₂ =10, taken from a Normal distribution with common variance, calculate the value of e so that P(S²/S24. The grades in an exam have a normal distribution with u=75 averages and o=8 standard deviation. The teacher gives AA to those who score 90 and above. Since 12 students got AA, what is the approximate number of students taking the exam?#27). Same question on both pictures. Do the part that’s blank.Q2: Let X and Y have a bivariate normal distribution with parameters 4, = 2 = 1, of = 16, af = 25 and p = 3. The value of P(-3Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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