A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by f(x) = Cxe-x/2 0 least 5 months? x > 0 x ≤ 0 what is the probability that the system functions for at

A random variable has density function f(x) = 1.6 - 1.2x, for 0≤ x ≤ 1. a) Calculate the variance of X. Var(X) = 0.4 b) Calculate the variance of g(X) = 4X + 1. Var(g(X)) = X

The proportion of people who respond to a certain​ mail-order solicitation is a random variable X having the following density function.   ​f(x) = 2(x+3)/7, 0<x<1, 0, elsewhere   Find the variance of X.

The weight of your pet is a [Select] [Select] discrete variable Continuous variable

The life expectancy of a smartphone's battery X in days is a continuous random variable with probability density function fx=6x1-x for 0 ≤ q x ≤ q 1. Find the probability that a smartphone chosen at random will have a life expectancy exceeding 12 hours.

The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .54 Px(X = 1) = .16 Px(X = 2) = .06 Px(X = 3) = .04 Px(X = 4) = .20 %3D i) Compute E(X). ii) Compute Var(X).

Please solve all parts

The probability density function of a discrete random variable X is given by the following table: Px(X = 0) = .073 Px(X = 1) = .117 %3D Px(X = 2) = .258 Px(X = 3) = .322 Px(X = 4) = .230 %3D i) Compute E(X). ii) Compute Var(X).

gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4

1. A continuous random variable X is defined by (3+x) f(x) - 3sxs-1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean 2. If the probability density function of random variable is given by f(x) = wch 1srs2 sech x a. Find the mean b. Find the total area 3. If the probability density function of random variable is given by f(x) = sinh 2x 1sxs2 a. Find the mean b. Find the total area c. Illustrate the graph (use bell shaped figure) II II