Statistics and Probability Answers

Given that u="\\chi"²_m and v="\\chi" _n² further let u and v be independent variables obtain the probability density of F=(U/M)/(V/N) where m and n are the df for U and V

Let X₁,X₂ and X₃ be random variables with equal variances but with correlation coefficients ρ₁₂=0.3,ρ₁₃=0.5,ρ₂₃=0.2 find the correlation coefficient of the linear function Y=X₁+X₂ and Y=X₂+X₃

Suppose that a man leaves for work between 8:00 a.m and 8:30 a.m and takes between 40 and 50 minutes to get to the oce. Let X denote the time of departure and let Y denote the time of travel. If we assume that these random variables are independent and uniformly distributed, find the probability that he arrives at the office before 9:00 a.m

Obtain linear regression equation of Y on X and X on Y for the bivariate function expressed as follows

f(x,y)={ 2/3(x+2y) 0<x<1 0<y<1

{ 0 otherwise

Let the independent random variables X₁ and X₂ be N(0,1) and "\\chi" ²(r) respectively. Let Y₁=X₁/(X₂)^(1/2)/r and Y₂=X₂

i) Find the joint pdf of Y₁ and Y₂

ii) Determine the marginal pdf of Y₁ and show that Y₁ has a t distribution

Suppose each of two boxes contains two identical balls marked with numbers 1 and 2. Two balls are selected at random, one from each box simultaneously. Let X denote the maximum of the numbers on the balls selected and Y the minimum of the numbers on the balls selected. Determine the joint probability distribution of X and Y

At XYZ University, another group of students was selected and asked how much of their weekly allowance they spent in buying mobile phone load. The following is the list of amounts spent: Php 200, 180, 30, 20, 10, 160, 150, 80. find the standard deviation

Given that the joint probability distribution of the discrete random variables X and Y is given by

f(x,y)= { k(4x+3y) x=1,2,3 y=1,2

{ 0 otherwise

Find

i) The value of the constant k

ii) The marginal probability distribution function X

iii)The conditional probability distribution Y given x=2

iv) The conditional mean given X=2

Differentiate between strong convergence of a random variable and weak convergence in probability

At ABC University, a group of students was selected and asked how much of their weekly allowance they spent in buying mobile phone load. The following is the list of amounts spent: Php 120, 110, 100, 200, 10, 90, 100, 100. find the standard deviation.