a) Let X₁, X₂, X3, ..., Xn be a random sample of size n from the normal distribution N(μ,²). i) State, with parameter(s), the probability distribution of 1) 2) X3-X2 o√2 1 (X4-X₁)² 2 02
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Xi ~ N(μ, σ2) ; i=1,2,..,n and random sample.
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- 2. Let X, X,.., x, be a random sample from a distribution with p.d.f. f(x;0)=0x, |>x>0 Is the MLE O EE of 0? AEE of 0?Suppose the random variable X follows a normal distribution with mean 80 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are A) -2 to 2 B) -3 to 3 C) -1 to 1 D) noneA1. Need help plz
- poisson distributiona) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?Q8 and Q9 please
- True False? a)A sided dice with the probability of 1 and 6 coming p and the other numbers (2, 3, 4, 5) is 2p is rolled n times. x̄, is the average of the numbers in n shots. According to this information, p = 2 / 5x̄. b)If X1, ..., Xn, N is a random sample drawn from the distribution (μ, ϭ²), the sample mean x̄ and sample variance S² are always independent.26 - The random variable Z has a standard normal distribution. Which of the following is the z value such that P(Z<z)=0.1379? a) 1.09 B) -0.05 NS) -2.11 D) -1.09 TO) 2.11x has continuous random variable is nomally distributed and average 40, standard deviation 10. So what is the probability of P (30