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- Let X be a continuous random variable with probability density function f(x) = 2(1-x), 0<=x <= 1. If Y = 2X - 1, find the probability density function of Y. x is lower case X is upper case. I need to get upper case of YSuppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e-x/1000 )/1000 for x > 0. Determine the the number of hours at which 12% of all components have failed. Please enter the answer to 2 decimal places.
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- If we consider the function f (x) = x2 (with x = position) as a probability density distribution defined at 0 ⩽ x ⩽ 3. Determine exactly the integral function F(x).Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.Find the probability density functions of non negative continuous random variables with failure rate functions (1) r(x) =x3 , (2) r(x) = 1/(1+x)
- the probability density function for a uniform distribution on the interval [1, 5] equals:Let X be exponentially distributed with parameter λ. Calculate the probability density of Y =(X−3)/(X+1). please provide some explanation with the taken steps, thank you in advance.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?