for the given density table: Y: 1 f(Y) 0.5 0.45 0.05 F(3)-F(2)=? (F is cumulative distribution...
Find E(Y), E(Y^2 ), E(Y^3 ), Var(Y) Problem 2.6.3 (variation of) The cumulative distribution function of the discrete random variable Y is given by the following table: y-10 Fy0 0.15 0.4 0.8 1 F(y) 0.1 0.15 0.4 0.8 1
3. The cumulative distribution function of a random variable Y is: 0 if y<-1, 0.3 if -1 y <0.5, 0.7 Fr (y)- y < 2, if 0.5 1 if y 2 2. (a) Draw a sketch plot of Fy (y) d) Find the probability mass function, fz(2), of Z -Y2 (e Find El2] and Var(Z) (f) Find El2-321 and Var(2-32). 13 marks]
consider continuous joint density function f(x,y)= (x+y)/7; 1<x<2, 1<y<3 Marginal density for Y? Select one: (2+3x)/14 (3+2y)/7 (2+3y)/14 (3+2y)/14 consider continuous joint density function f(x,y)= (x+y)/7 ; 1<x<2, 1<y<3 P(0<x<3, 0<y<4)=? Select one: 0.5 1 0.15 0.25
Problem 2: Let Y be the density function given by f(y) = 1.5, -1<y < 0, { 1-cy, 0 <y <1 10, elsewhere. (1) Find the value of c that makes f(y) a density function. (2) Find Fy). (3) Compute Pr(-0.5 <Y <0.5) (4) Graph f(y) and F(y) in the same rectangular coordinate system. (5) Find the expected value u = E[Y]. (6) Find the variance o2 = Var(Y) and the standard deviation o of Y.
Problem 2 If the cumulative distribution function of X is given by o F(b) = b<0 0<b<1 1<b<2 2<b<3 3<b<3.5 b> 3.5 1 calculate the probability mass function of X.
Question#3 20 Points Let Y has the density function which is given below: 0.2 -kyS0 f(v) 0.2 + cy 0 0<p 1 otherwise (a) Find the value of c. (b) Find the cumulative distribution function F(y). (c) Use F(y) in part b to find F(-1), F(0), F(1) (d) Find P(0sYs0.5) (e) Find mean and variance of Y d X1 amd 2 aild ate subarea of a fixed size, a reasonable model for (X1, X2) is given by 1 0sx1 S...
Question #48 F(y) = Let Y be a continuous random variable with the following cumulative distribution function: for y sa 1 -e-0.5(-a), for y> a where a is a constant. What is the 75th percentile of Y?! F 0, Possible Answers (A F(0.75) Ba-V2ln(4/3) Ca+V2ln(4/3) Da-2Vin2 [E]a +2 Vina
1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y. (4) E(X) 1) Assume that the joint cumulative distribution of (X,Y) is x F(x, y) A(B+ arctan(C+arctan Find (1) the efficiency of A B C (2) the joint probability density function of (X,Y). (3) determine the independence of X and Y....
A joint probabilty mass table is given as follows: 0 0.15 0.25 1 0.45 0.15 1) Choose the correct marginal PMFs for X and Y. P(z) P() 0 0.15 0.45 1 0.25 0.5 P(z) P() 0 0.40.6 1 0.6 0.4 0 0.6 0.4 1 0.4 0.6 2) Find P(X-01Y 0) 0.250 0.375 0.667 3) Find P(Y-11 X 0) 0 0.375 0.417 0.625 | О 0.750
Assume that the joint density function of X and Y is given by f (x, y) = 4,0 < x < 2,0 < y = 2 and f (x, y) = 0 elsewhere. (a) Find P (X < 1, Y > 1). (b) Find the joint cumulative distribution function F(x, y) of the two random variables. Include all the regions. (c) Find P (X<Y). (d) Explain how the value of P (1 < X < 2,1 < Y < 2)...