A continuous random variable X that can assume values between x = 3 and x = 8 has a density function given by 2(1+x) f(x) = Find (a) P(X <7); (b) P(5≤X<7). 65 |(a) P(X <7) = (Type an integer or a simplified fraction.) (b) P(5≤X<7)= (Type an integer or a simplified fraction.)
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- Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.1. A continuous random variable X is defined by (3+x) f(x) - 3 sxs- 1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean II2. Let f(x) = 3x(x² − 1) (x³ + 2x + 3) (a) Use distribution to expand the function. (b) Use the rules in from the table above to differentiate the function.
- X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osx55 otherwise Find : (a) the constant k; (b) P(15XS 2); (c) (d (e) (f) E(X); E(3X + 1); E(X?); Var (X); (g) Var (4X - 5);9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): 3 f (x) ={32 (x- 2)(6-x) for2A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?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 IIWhich of the following is the correct sum of squared residuals to be minimized to find (2x-1)-b the fit f (x) = using a data set {(xo,Yo), (x1, y1), .., (xn, Yn)} ? A.) E-o(In(y;) + a – b2x; + 1)2 B.) E-o(In(y;) + In a + b In(2x¡ - 1))² C.) E-o(Vi - (2x1-1)-, a D.) E-o(In(yi) – In a – b In(2x – 1))? E.) E-o(In(y;) + In a – b2x + 1)?. Let Y be a continuous random variable where f(y) F(y)? (a) Y 18 Y 15 Y-3 18 Y+3 (b) (c) (d) 18 (e) None of the above = 1 18 -3 ≤ y ≤ 15. What isIF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variable3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?SEE MORE QUESTIONS