(f) 14X- Y +5.2.3 Consider a sequence of independent random variables X¡,each with a standard normal distribution.(a) What is P(X,|<0.5)?(b) If X is the average of eight of these random variables,what is P(X|< 0.5)?(c) In general, if X is the average of n of these randomvariables, what is the smallest value of n for whichP(IX| < 0.5) 2 0.99?

Xi's are independently distributed standard normal random variable. So, Xi ~ N(0,1) If n number of…

Answered: 5.2.3 Consider a sequence ôl each with…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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15. A random variable X has a mean ? = 10 and a variance ? 2 = 4. Using Chebychev’s inequality, find:(a) ?(|? − 10| ≥ 3)
4. Let X₁ N (0,3²), X₂ N(4,4²), and X3 ~ N(-1,22) be independent random variables. Find P (X₁ + X₂ +3X3 <-8), using the table for standard normal distribution.
Page 348 5.3.14
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
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?
ONLY Q8
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.
13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(205
11th -The variance of the sample formed by the sample averages of the samples randomly taken from a population with the condition of substitution, with a size of n=100, was found to be 0.01. What is the sample standard error value?a)0.001 B)0.014 NS)0.20 D)0.032 TO)0.10
X 1. A random variable is given by the table -2 1 3 4 P(X) | 0,2 | c | 0,3 | 0,1 Find constant c and then the mean value and variation.
10. Let x be a binomial random variable with n = 150 and p = 0.4. Use the normal approximation to find the following. a) P(48 69) P(X>69) = 1- P(X = 69.5) = 1−ø(- c) P(X ≤ 70) 70.5-60. 69.5–60. 6 P(X <=70) = P(X = 70.5) = (- -) = = 0.9599 -) = 0.0571

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