1. The error, X, in measuring the length of a rivet (in micrometers) has the following probability density functionf(x)=20-x-(3-X)³ for 0 ≤ x ≤ 3 and 0 otherwise.243g) What is the expected value of x² ?h) What is the probability that X is greater than its expected value?i) What is the expected value of X³-3X+1?Please solution USING R script

A random variable X has following probability density function: fx=20243 x3-x3 ; 0≤x≤3 By…

Answered: 1. The error, X, in measuring the…

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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People with high blood pressure suffer from hypertension. Data on fasting blood sugar (milligrams/deciliter) and magnesium (milligrams/deciliter) in blood specimens collected from 60 patients diagnosed with hypertension were collected. The accompanying technology printout gives 90% confidence intervals for the mean fasting blood sugar (FBS) and mean magnesium level (MAG). Use this information to complete parts a through d below. Variable FBS MAG N 60 60 Mean 102.11 1.85238 StDev 38.91 0.05472 90% CI SE Mean 5.02 ( 93.72, 110.50 ) 0.00706 (1.84058, 1.86418) a. Locate and interpret the 90% confidence interval for mean fasting blood sugar on the printout. (Type integers or decimals. Do not round.) O A. The 90% confidence interval for mean fasting blood sugar indicates that 90% of all hypertensive patients will have a fasting blood sugar level between O B. The 90% confidence interval for mean fasting blood sugar indicates that 90% of hypertensive patients in the sample had a fasting blood…
EX#1: Let the continuous random variable X denote the current measured in a wire in milliamperes. Assume that the range of X is [4.9,5.1] mA, and assume that the probability density function of X is f (x) = 5 for 4.9 < x < 5.1. Calculate the mean, variance and standard deviation.
The probability density curve of a random variable X is given in the following figure. The possible values for X range from 20 to 50.
Let X be a continuous random variable whose probability density function is given by the formula if 0 < x < 5 2x if 5 ≤ x ≤8 otherwise. 1 20 HP = ← p(x) Find the probability that X is between 3 and 7. Enter the exact answer as a fraction (not a decimal approximation).
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 195x, (0,5] 2, [0,5] 125 a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)
Based on this density, what is the probability that X is between 0.5 and 1.5? Possible answers are 1/2, 1, 1/3, 3/4. Please show steps on how answer was obtained.
6.106 If Y is a continuous random variable with distribution function F(y), find the probability density function of U = F(Y).
According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21
For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <
The amount of time, X, in minutes that it takes a rat to navigate a maze has the following probability density function: f(x)=(x − 1)²(4 - x) for 1 ≤ x ≤ 4 and 0 otherwise. 27 1 a) What is the probability that X > 2.5? 2 b) What is the probability that X < 2.5? c) What is the probability that 1.25 < X < 2.75? d) What is the expected value of X? 4 e) What is the expected value of X - 3? 5 f) What is the expected value of 3X? 7 g) What is the expected value of x²? h) What is the probability that X is less than its expected value? i) What is the expected value of √X?! 9 8 j) What is the 70th percentile of X? 10 k) What is the probability that X is within 0.1 of its expected value? 11 1) What is the probability that X = 0.7? 12

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