Continuous variable X is uniformly distributed the interval [2.3,34.8]. The density function given by fy (y) = 1/12.3, 0≤ y ≤ 12.3 and fy (y) = 0, otherwise.
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- Find the distribution function and density function of Y = sinX, where X is distributeduniformly between 0 and 2π.Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.The time between successive clicks on an ad has a density function fX(x) = 2e^(−2x), x ≥ 0 and f = 0 otherwise. Find the standard deviation σX.
- If X is uniformly distributed over (0,1), find the density function of Y = eXA continuous random variable X that can assume values between x=2 and x=4 has a density function given by f(x)=12. (a) Show that the area under the curve is equal to 1. (b) Find P(3<X<3.3). (c) Find P(X≤3.9).For random variables X and Y with joint density function f(x,y) = 6e^-2x-3y. (x,y > 0) and f(x,y) = 0 otherwise, find: Are X and Y independent? Give a reason for your answer.
- A uniformly distributed continuous random variable is defined by the density function f(x) = 0.2 on the interval [2, 7] . The value P(x > 4) = _____________. 0.1 0.2 0.4 0.6The joint probability density function of X and Y is constant over the shaded region in the attached graph, and otherwise = 0. a) Find the value of f (x, y) for (x, y) inside the shaded region. b) Find the probability that both X and Y are between 0 and 1.A continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = ½ a) Show that the area under the curve is equal to 1 b) Find P(2 < x < 2.25) c) Find P(x < 1.6)
- Consider the functionf(x)=1/x, defined on the interval 1≤ x≤ e describe the shape of distribution after graphing the density function.A random variable X has probability density function (pdf) fx(x), wherefx(x) =and k is a constant. Find:i. kii. P [ X > 1]iii. the mean of XThe random variable X has the Cauchy density f(x) = 1/π(1+x2) for −∞ < x < ∞. Find the probability density of the random variable Y = 1/X . KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION