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 po...

Question

Question

Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is,

A) Find f_Y1 and show that the area under this is one

B) Find P(Y₁ > 1/2)

Answer 1

Answer #1

olution:- PCY Y2) SSCY2ddy2 > dde STT So, is I The probabiliy PCy>Ya) Soanned with aur CamScanner

Answer 2

Similar Homework Help Questions

Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2)...

Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
Statistics - Introduction to Probability Please show all work Let Y1 and Y2 be continuous random...

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 Y1 have the joint probability density function given by and Y2 k(1 y2), 0 s...

Let Y1 have the joint probability density function given by and Y2 k(1 y2), 0 s y1 y2 1, lo, = elsewhere. (a) Find the value of k that makes this a probability density function k = (b) Find P 1 (Round your answer to four decimal places.)

Need Answer only.. Send me fast. with clear writing. QUESTION 12 Let Y1 and Y2 be...

Need Answer only.. Send me fast. with clear writing. QUESTION 12 Let Y1 and Y2 be continuous random variables with the joint p.d.f. (probability density function) f(V1, V2) given by 23 v 2² v2 V1 V2 for -2 S Vis 1 and 0 Sy2 si fly1, y2) = 0 elsewhere Find the joint c.d.f. (cumulative distribution function) of the bivariate random variables Y1 and Y2 os 2 0 2 3 1 2 ² 1 2 o (v?? + 8) vz?
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1,...

2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
Let (X1, Y1) and (X2, Y2) be independent and identically distributed continuous bivariate random variables with joint pr...

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) .

Problem 4 Let Yı, Y2, ..., Y, denote a random sample from the probability density function...

Problem 4 Let Yı, Y2, ..., Y, denote a random sample from the probability density function (0 + 1)ye f(0) = 0 <y <1,0 > -1 elsewhere Find the MLE for .
Consider two random variables with joint density fY1,Y2(y1,y2) =(2(1−y2) 0 ≤ y1 ≤ c,0 ≤ y2...

Consider two random variables with joint density fY1,Y2(y1,y2) =(2(1−y2) 0 ≤ y1 ≤ c,0 ≤ y2 ≤ c 0 otherwise (a) Find a value for c. (4 marks) (b) Derive the density function of Z = Y1Y2. (10 marks) . Consider two random variables with joint density fyiy(91, y2) = 2(1 - y2) 0<n<C,0<42 <c o otherwise (a) Find a value for c. (4 marks) (b) Derive the density function of Z=Y Y. (10 marks)
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a...

. Suppose the Y1, Y2, · · · , Yn denote a random sample from a population with Rayleigh distribution (Weibull distribution with parameters 2, θ) with density function f(y|θ) = 2y θ e −y 2/θ, θ > 0, y > 0 Consider the estimators ˆθ1 = Y(1) = min{Y1, Y2, · · · , Yn}, and ˆθ2 = 1 n Xn i=1 Y 2 i . ii) (10 points) Determine if ˆθ1 and ˆθ2 are unbiased estimators, and in...

Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1...

Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1 = 0 otherwise (a) (8 pts) Calculate Cov(Y1, Y2). (b) (3 pts) Are Y1 and Y2 are independent? Prove your answer rigorously. (c) (6 pts) Find the conditional mean E(Y2|Y1 = 1). 3