Consider the following joint density function: f(x, y) =÷(x+3y2), 0
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- The joint density function of X and Y is given by f(x, y) = xe-(x+y) x > 0, y > 0 0 otherwise What is P(x < 1, y < 1)? Question 20 options: a 2e-2 b -e-1 c e-1 d -2e-2Question 30: Find K such that f(x)= ke^(x) is a probability density function over the interval[0,2]. Then write the probability density function. Question 31: Find the volume generated by rotating about the x-axia the regions bounded by the following:One-dimensional objects Find the mass and center of mass of the thin rods with the following density function. ρ(x) = 1 + sin x, for 0 ≤ x ≤ π
- A joint density function is given by f (x, y) = kx 0 < x < 1, 0 < y < 1 where k is a constant. (a) Find Corr(X, Y ). (b) Find f (x |y)Findi) The joint density function of ?1 and ?2ii) ?(?1 >1, ?2 > 1) iii) ?(?2 < 5)The density function is often used as a model for the lengths of life of physical systems. Suppose Y has the Weibull density just given. Find: a) the density function of U = Ym b) E(Yk) for any positive integer k
- One-dimensional objects Find the mass and center of mass of the thin rods with the following density function. ρ(x) = 1 + x3, for 0 ≤ x ≤ 1A random variable Y has the density function a) Find E [e^(3Y/2)].b) Find the moment-generating function for Y .c) Use the moment-generating function of Y to find E (Y) and V (Y)."Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.
- a.) Define the constant c ∈ ƒ so that the function f is a density function. In addition, define the accumulation function FX of X. (b) What is the distribution of the transformation Y = ln X? (c) Specify EY and VarY. The function is as a screenshot in the attachment, as I didn't know how to write is to this fieldIf the density function of X is (x) = {8 0 < x < 4 0.w Find the probability mass function of Y = [X] (Where [.) denotes the Floor function), then find E(Y).Suppose you choose a real number X from the interval [2, 10] with a density function of the form f(x) = Cx, where C is a constant.(a) Find C.(b) Find P(E), where E = [a, b] is a subinterval of [2, 10].(c) Find P(X > 5), P(X < 7), and P(X2 − 12X + 35 > 0).