Consider the probability distribution function (PDF)f(x) 3 Ax sin x, for 0 sx s(a) Consider whether f is a PDF. If it is not. what value of A will make it so?(b) Find P(0 sXs1/2).(c) Find the average value of x.BIUGGNext262 Type here to searchenovoSHOT ON REDMI Y3AI DUAL CAMERAE.

For a continuous random variable, X, with probability distribution fx, the relation ∫-∞∞fxdx=1 holds…

Answered: Consider the probability distribution…

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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The probability density function of the random variable X is as in the picture with λ> 0. Find the moments estimator (λ^) of the parameter λ.
On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X exceeds 1.8 micrometers?
The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X is less than 3.8 micrometers?
While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove x kilometers from home (along the road) is p(x)=7e−7x for x≥0 What is the probability that you dropped it within 1 kilometer of home?
While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove x kilometers from home (along the road) is p(x)=7e−7x for x≥0 At what distance y from home is the probability that you dropped it within y km of home equal to 0.95?
If X has an exponential distribution with the param-eter θ, use the distribution function technique to find the probability density of the random variableY = ln X.
The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?
Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
The probability density function of a random variable X is given by Find the probability that it will take on a value within two standard deviations of the mean andcompare this probability with the lower bound provided by Chebyshev’s theorem.
A continuous random variable has the probability density function f(x) = 1/8 for 0 ≤ x ≤ 8. What is the expected value of X?
If X is a random variable that is uniformly distributed between -1 to 1, find the PDF √|X| of and pdf of -ln|X|

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Consider the probability distribution function (PDF) f(x) = Ax sin x, for 0 sxsn (a) Consider whether f is a PDF. If it is not. what value of A will make it so? (b) Find P(0 sx s 7/2). (c) Find the average value of x.