A continuous random variable X that can assume values between x=1 and x=6 has a density function given by ​f(x)=15.  For this density​ function, find​ F(x). Use it to evaluate ​P(2 ____)

let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) =3x² for 0 ≤ x ≤ 1. Find the mean and variance of X. Interpret the results.

The probability density function of X, the lifetime of a certain type of device (measured in months), is given by Find the following: P(X > 34) = The cumulative distribution function of X: F(x) = {8 if x 25 if x 25 if x 25 f(x) = 25 if x 25 x2 The probability that at least one out of 6 devices of this type will function for at least 34 months:

Use the following to answer the next 3 questions. The random variable X is described by the following pdf: f(x) = {3x 3x-4, x > 1 otherwise 19. What the cumulative density function? a. F(x) = 1 b. F(x) = -3 -x-³ c. F(x): = 1-x-3 d. F(x) = 3x¯4 20. What is the probability X will be less than 1.2? a. 0.634 b. 0.421 c. 0.579 d. 0.113 21. What value represents the 95th percentile? a. 2.71 b. 1.65 c. 1.96 d. 1.17