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.243j) What is the 55th percentile of X?k) What is the probability that X is within 0.4 of its expected value?1) What is the probability that X = 2?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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The waiting time at a local oil changing station is uniformly distributed between 15 and 20 minutes. what values does the probability density function takes on over the interval between 15 to 20?
A continuous random variable has the probability density function of f(x)=0.0118x and the interval of [O 13]. What is the probability that this variable has a value between 1 and 2? Answer: A continuous random variable has the probability density function of f(x)=0.0118x and the interval of [O 13]. What is the cumulative distribution function for the value of 3? Answer:
Data are obtained on the location of incidents on a 12-kilometer-long bridge. The distribution of the distance along the bridge (in kilometers) where an incident occurs is depicted in the density curve below. 12 Distance (kilometers) along the bridge where an accident occurs 12 1. The probability of an incident that occurs in any 4 kilometers long bridge segment is always distributed over any 4-kilometer interval. A. 1/3, uniformly B. 1/3, not uniformly C. 1/6, uniformly D. 1/2, not uniformly To put it another way, the probability is 2. What is P(9 < X < 12)? 1 Same as P(2 < X < 5). 2. Same as P(2 s X < 5). 3. Same as P(2 < X < 5). 4. Same as P(2 < X < 5). A. 1 B. 1 and 2 C. 2, 3, and 4 D. 1. 2. 3, and 4
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).
The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following probability density function: f(x)= 338 x3 for x ≥ 13 and 0 otherwise. j) What is the 50th percentile of X? k) What is the probability that X is within 1 of its expected value? l) What is the probability that X = 15?
Ff.291.
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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