Question

A scientist collected 12 observations on ( X , Y ), and got the following results:

                             ∑ x_i = 60 ,        ∑ y_i = 42 ,        ∑ x_i y_i  = 102 ,       S_xx = 90 .

         What is the y-intercept of the regression line for these data?

Let X be a continuous random variable with the probability density function:

          f (x) = c ( 1 - x² ) ,    -1 < x < 1.       What is the expected value of X² ?

                            (a)   0.1                   (b)   0.2                      (c)   0.3                      (d)   0.4                      (e)   0.5   

Let X be a continuous random variable with the probability density function:

             f (x) = x64   ,    0 < x < c.       What is the median of X ?

                            (a)   5.6                     (b)   6.4                  (c)   7.2                      (d)   8.0                    (e)   8.8   

Answer 1

и с (од = = Griven N=12 3 - Go - Час Enigi 15 and Sxx = 90 Let to be the slope and a ke l y tulip , lim 2 ЧХ - пX9 b- Sx и where da xi eta Бо 5 W and у : 29 Иа 7 И la - Then, bi 10a - axsr=) ар (0a - Во ОО

3 b = -108 90 -: 6 =-1.2 Then, - Z Q a = T-bæ +(1.2x5) = 3.8 +6 - 9.5 Hencer y.ulizcepto of fią reqsession line as a= 9.5

Let x be a continuous raudon variable with pdf as) fo= (1-x²) -12X</ is a palf than a Hercr feer I faldx = c f(-x2) dx -1 -1 こ بره (32 - ) » 20 = 2 (x - 22 =201-5 =we Theur WC 1 3 = 2 3

Then, the paf of xas, $60) = Ž (1-x2) = -1841 Then E(x) = 8 x farbe 22 (1-22) da 6 sa2 24 dx 23 X 3 S (Ő-) ah lelo lelo 0.2 Auswer: 6 0.2

Let x be a continuous randon variable with pelf as a o LxLc x for = 64 Let M be the median of x rhen, Foidx= 5x dx = [32] M = 1 / töy 117 - stu ㅗ is 6th ㅗ g 5 M2=64 M=8 Herce median of xow) M=0 Ausger @ 0.0