Suppose that X is a continuous random variable with density function f(x). If f(x)=k for -3 ≤ x ≤ 2 and f(x) = 0 otherwise, determine the value of k. 2 25 A. B. C. E. 3 10 1 10 1 5 7 25
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- Given that random variable X is continuous type , we form the random variable Y as Y = g (x) = 6 F, (x) + 4. Then f, (y) is %3D ON(6, 4) ON (4, 6) O U (4, 10) OU (6, 10)Let fxr(r, y) be the joint probability function for the random vector (X, Y). Which of the following staterment is INCORRECT? If both X and Y are discrete random variables, then for any set (aj...,an,b} CR. we must have H ÁXY(4, b) 0, we must have E(Y X = a) = E(Y). If X and Y are independent, then for any a, be R. fxx(a,b) > 0 implies both fx(a) > 0 and fy(b) > 0. Previous Save For Later Nextb) The continuous random variable Y has the following probability density function. Pembolehubah rawak selanjar Y mempunyai fungsi ketumpatan kebarangkalian seperti berikut. Jh(3y² +2) ; -2sys2 0 ; otherwise f(y)={ 1 Show that h=- 24 i. 1 Tunjukkan bahawa h=; 24 ii. Based on the value in part (i), find the cumulative distribution function F(y). Berdasarkan nilai dalam bahagian (i), cari fungsi taburan longgokan F(y).
- The probability density function (p.d.f.) of a continuous random variable X is defined to be: kx + for 0 < x < 1 f(x) = |0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the value of k that makes the above function a proper p.d.f. Part b) Find E(X).Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0Show the density func in table form and show complete solution.I want the full answer with steps for c,d and e1. Let X and Y be two jointly continuous random variables with joint pdf f(x,y) = {k(x + y), 0≤x≤ 1,0 ≤ y ≤1 otherwiseThe joint p.d.f of two random variables X and Y is given by 1. ƒ(x, y) = = x(x − y),0 < x < 2,− x < ySuppose that the distribution function of X is given by: (0, b<0 b Osb<1 1 b F(b) =- D=1, Isb<2 2 11 2sb<3 12 b23 1. Determine its corresponding probability mass function. 3 2. FindIf X is the continuous random variable whose probability density function, Find P(X25) for 0≤x≤ 4 f(x) otherwise 0 O 1 -1 Do not existRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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