A continuous random variable Z has a probability density function f(z) = Find the following: a) P(Z > 1.2) b) P(0.6 ≤ Z≤ 1) (0.25z³, 0≤x≤2 elsewhere (0,
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- 3. For some c, a continuous random variable X has density (a.) What is c? (b.) Find ux and o. f(x) = { £, for1≤2≤4 0, otherwiseQ1: Let X be a random variable with probability density function (PDF) given by Find the following: 1) P(x ≤ 1/2) 2) P(x ≥ 0) 3) P(1.2 ≤ x ≤ 2) Compute CDF 4) 5) Plot CDF for 0≤x≤1 2- x, for 1 < x≤2 otherwise x, Mer={2-4. f(x) =b) 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).
- 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 0Let X and Y be continuous random variables with joint p.d.f. f(x, y) = k(x + y), 0≤x≤y≤1 Find the (a) (b) (c) (d) (a) value of the constant k joint c.d.f of X and Y F(x, y) marginal c.d.f. of X and marginal c.d.f. of Y. marginal p.d.f. of X and marginal p.d.f. of Y. Given that X is a continuous r.v. with p.d.f. kx-(0+1) x>α; 0>0, a>The PDF of a random variable Y is Sy/2 0For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.292. A random variable X has a probability mass function given by: 1 0.2 a. Determine P(x) = 2 b.Find P(X<2) c. Find P(X≥ 3) X P(x) 0 0.1 2 ? 3 0.4b) A random variable Xhas probability density function. [Cx(1-x), 0≤x≤1 fx(x) = 3 in) Find [x²] 2 i) Find C. ii) Find P CS Scanned with CamScanner 076, elsewhereLet X₁,..., Xn be a random sample from a continuous distribution with the probability density function fx(x; 0) = [3(x−0)², 0≤x≤0 +1, otherwise 0, Here, is an unknown parameter. Assume that the sample size n = 10 and the observed data are 1.46, 1.72, 1.54, 1.75, 1.77, 1.15, 1.60, 1.76, 1.62, 1.57 =The probability density function of the discrete random variable x; x = 1,2,3 8 - f(x dd(other cases) olarak tanımla is defined as. Calculate the expected value of x accordingly. O A) 1/6 OB) 2 O C) 7/3 OD) 5/2 OE) 3/5A continuous random variable X has density given by: f(x)= {1/2, -0.5≤x<0.5 {1, 0.5≤x≤1 {0 Based on this information, answer each alternative. a. P(X< −0.39 or X≥0.74): b. P(X≥−0.01): c. P(0.34≤X≤0.79): d. P(X≥0.36|X≤0.99): e. P(X≤0.63|X≥0.31):SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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