STA 2023 Homework 2 | Complete Solution

STA 2023 Homework 2
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. What is R
2
in the least squared regression?(10’)
V. Interpret the meaning of slope and intercept?(10’)