A random variable x has a density function f(x) = c(x+1) where 0 < x < 2| 2
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- Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.The number X is chosen at random between 0 and 1. determine the density functions of the random variables V = X/(1 - X) and W = X(1 - X)Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability Theory
- A random variable X has the density function 1 fx (x) = for - 3 1) (c) P(X + 3 > 4)1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.
- Consider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)The time until a chemical reaction is complete (in milliseconds) has the density function -x/100 f(x) = for x > 0. 100 a) Determine the mean and variance of X. b) P(X > 200).Suppose you have two independent random variables X ~ Y ~ Exponential(A2), A1 > 0, d2 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P( > 1). (c) P(X +Y > 1).
- Y has a density function + y, Osys1, Ry) = {7 0, elsewhere. Find the mean and variance of Y. (Round your answers to four decimal places.) E(Y) = V(Y) =Exp(2), compute the If X is an exponential random variable with parameter A = 2, i.e., X ~ probability density function of the random variable Y = In X.The random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.