Let X1,..., Xn, Xn+1 be a random sample of size n +1 from a N(µ, o²) distribution. Finda constant c such that the statisticX – Xn+1C-Shas a t distribution.In the framework of Exercise 5 supposen=8. Determine k such thatP(X – kS < X, < X + kS) = 0.80

The mean of the random variable is defined as X¯=∑i=1nXi. The sample standard deviation is defined…

Answered: Let X1, . .. , Xn, Xn+1 be a random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
Let Y₁, Y2, Y3, Y₁, Y5 be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁² + Y₂² + 3Y3²+ Y₂² +4Y5² Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X2,..., X, be independent and normally distributed random samples from populations with means ₁ = 2 and ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of 0₂² = k.
Let X be a random variable with a uniform distribution over the interval [-3,6]. Determine the mean of X. [The answer should be a number rounded to five decimal places, don't use symbols such as %]
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Let X1,X2.,X, and Y1,Y2,.Yn be two random sample of size n from a normal independent distributions Var(X)=1 and Var(Y)=20?. Let U = E-1(X; – X)² and W = E1(Y; – Y)? W a. What is the sampling distribution of the statistic U + 202 b. If the 90th percentile of the statistic (U + 202 is 33.20, what is the sample size n?
x = 1,2,...,9. (This 2. Let X be a discrete random variable with pmf f(x) = log₁0 distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
Q4: Let i denote the mean of a random sample of size 25 from a gamma type distribution with a = 4 and p > 0. Then 1. 1. E(x) = 48 and Var(x) = 48² O True O False 2. I~N (4B, 4B²) 25 2. O True O False
a) 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?
Let Zw distributed as Chi square random variable with n degree of freedom. Find the limiting distribution of Wn = Zw/n2
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Let X1, . .. , Xn, Xn+1 be a random sample of size n +1 from a N(µ, o²) distribution. Find a constant c such that the statistic X – Xn+1 S has a t distribution. In the framework of Exercise 5 suppose n = 8. Determine k such that P(X – kS < X9 < X + kS) = 0.80