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- Determine dimension x to 3 decimal places.Suppose 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.Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?
- 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.Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable on the interval 30 ≤ x ≤ 50 with density function f(x) = 1/20, 30 ≤ x ≤ 50. Find the probability that a battery selected at random will last at least 35 hours.Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.
- Suppose X1, X2, X3 denote a random sample from the exponential distribution with density function. Please at the image for the full questions.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.Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a) According to Chebychef’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(|x − µ| <2 ∗ σ) b) What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?
- Suppose the duration (in hours) of a certain valve is a random variableX with density function f(x) = 648x−4 for x > 6, and zero otherwise. What's the time expected life (in hours) of this valve?Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF, denoted f, is given by f ( x ) = c ( 25 − x^2 ) , − 5 ≤ x ≤ 5 , and where c is a positive normalizing constant. What is the expected value of X^2?Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would: Have the same height but one would be shifted 4 units to the right. Have no horizontal displacement but one would be flatter than the other. Have no horizontal displacement but one would be steeper that the other.