Consider the probability density function fx (x) = a e-b lel where X is the ran variable which assumes all the values from (i) relation between a and b ii) the probability of finding X in the range 1 to 2. -00 to -o, Find
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- Figure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.The continuous random variable XX has a probability density function (pdf) given by Part(d) Find Var(X), correct to 2 decimal places Part(e) Find the median of X, correct to 2 decimal places.Part(f) Find E(X), correct to 2 decimal placesSuppose 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.
- A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of xA variable X is distributed at random between the values 0 and 4 and its probability density function is given by: f(x) = kx³ (4- x)². Find the value of k, the mean and standard deviation of the distribution.
- Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-, 0) is a function f such that f(x) > 0 and | f(x) = 1. -0- (a) Determine which of the following functions are probability density functions on the (-00, 00). 0 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event – if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. S xf (x) dx yields the expected value for a density f (x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-0, 0) is a function f such that f(x) > 0 and | f(x) = 1. %3D (a) Determine which of the following functions are probability density functions on the (-0, 00). (i) ƒ(x) = 0. ə > x > 0 1-x] otherwise -2 0 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. Srf(x) dx yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.