Need Answer only.. Send me fast. with clear writing.
Need Answer only.. Send me fast. with clear writing. QUESTION 12 Let Y1 and Y2 be...
Statistics - Introduction to Probability
Please show all work
Let Y1 and Y2 be continuous random variables with the joint p.d.f. (probability density function) f(V1, V2) given by Vi + V2 for Os Visl and O SV2 s 1 f(V1, V2) { 0 elsewhere Find the marginal c.d.f. (cumulative distribution function) of a random variable Y1
Let (X1, Y1) and (X2, Y2) be independent and identically distributed continuous bivariate random variables with joint probability density function: fX,Y (x,y) = e-y, 0 <x<y< ; =0 , elsewhere. Evaluate P( X2>X1, Y2>Y1) + P (X2 <X1, Y2<Y1) .
A) Find fY1 and show that the area under this is
one
B) Find P(Y1 > 1/2)
Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, Y1 and Y2 have a joint density function given by 1 yiy f(y, y2) 0, - elsewhere
Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin....
Let Y1<Y2<...<Yn be the
order statistics of a random sample of size n from the distribution
having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following
questions.
(a) decide whether Z1 = Y2
and Z2=Y4-Y2 are
stochastically independent or not. (hint. first find the joint
p.d.f. of Y2 and Y4)
(b) show that
Z1 = nY1, Z2=
(n-1)(Y2-Y1),
Z3=(n-2)(Y3-Y2), ....,
Zn=Yn-Yn-1
are stocahstically
independent and that each Zi has the exponential
distribution.(hint use change of variable technique)
The management at a fast-food outlet is interested in the joint behavior of the randomvariables Y1 , defined as the total time between a customer’s arrival at the store and departurefrom the service window, and Y2 , the time a customer waits in line before reaching the servicewindow. Because Y1 includes the time a customer waits in line, we must have Y Y 1 2 ≥ . Therelative frequency distribution of observed values of Y1 and Y2 can be modeled...
(Q6) The management at a fast-food outlet is interested in the joint behaviour of the random variables Yı, defined as the total time between a customer's arrival at the store and departure from the service window, and Y2, the time a customer waits in line before reaching the service window. Because Yſ includes the time a customer waits in line, we must have Yi > Y. The relative frequency distribution of observed values of Yi and Y2 can be modelled...