STA 2023 Homework 2 Deadline: 2/16/2015 Notice: Only paper version will be accepted. Name: Problem 1 (50 points) Suppose X is a random variable with probability: P(X=1)=0.4, P(X=5)=0.3, P(X=11)=0.1, P(X=15)=0.2 A. What is possible value of X? Write the distribution table for X.(5') B. What is the expected value, variance and standard deviation of X?(20') Suppose X is a random variable with binomial distribution b(6,0.6): C. What is P(X=0), P(X=1), P(X=2), P(X=3), P(X=4), P(X=5), P(X=6), P(X=7)?(10') D. What is the expect value, variance and standard deviation of X?(15') Problem 2 (50 points) We know from data that the time that the age of teens are positive associated with their weight. Your task is to report on the nature of this relationship. X = the age of teens = 16 Sx = 2 Y = the weight of teens = 100 Sy = 40 r = 0.9 I. Calculate the slope and the intercept of the regression line(10') II. Write down the equation of the regression line (10') III. Suppose a teen is 15 years olds, what is the weight you expect him/her to have?(10') IV. 2 What is R in the least squared regression?(10') V. Interpret the meaning of slope and intercept?(10')