Find the cumulative distribution function for the probability density function f(x) = on the interval [2,5]. 39 .. F(x) =|
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- A sample (X1, ..., X10) is drawn from a distribution with a probability density function. The sum of all 10 observations equals 150.(a) Estimate θ by the method of moments.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 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 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?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?Write down the probability density function of the umiformly distributed random variable X defined on the interval [0,5] and sketch the graph of the PDF of X.
- 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?the probability density function for a uniform distribution on the interval [1, 5] equals: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.
- The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density functionA continuous random variable X has a uniform distribution on the interval [−3,3]. Sketch the graph of its density function.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.