Probability and Statistics: Random Variables

The random variable T has a mean of ______ and variance of 16.

The expectation of X is ______, and the standard deviation of X is 9.

The survey of ______ residents provided the following information about the flu vaccine.

The probability of choosing a person who has no flu is ______.

The pharmaceutical company uses a random variable X which has a ______ density function.

The assignment must be done in ______ and submitted to the class rep before the deadline.

Assignment 1: STAT 166 Introduction to Probability and Statistics

Question 1: Random Variable T

Random variable T has a mean of 5 and variance of 16
Need to find the sum of constants "c + d" such that E(cT + d) = 100 and Var(cT + d) = 144

Question 2: Expectation of X

Expectation of X is -2
Standard deviation of X is 9
Need to find the value of E(x2 + 6)

Question 3: Flu Vaccine Survey

Survey of 1000 residents in a small community
Information provided:
- No vaccine: 24 flu, 289 no flu
- One shot: 9 flu, 100 no flu
- Two shot: 13 flu, 565 no flu
Questions to answer:
- a. Probability of choosing a person who has no flu
- b. Probability of a person having flu given no vaccine
- c. Probability of a person having no flu given two shots
- d. Proportion of the sample with no vaccine
- e. Probability of a person having no flu given no vaccine

Question 4: Pharmaceutical Company Chemical Usage

Total amount of chemical used in a month is a random variable X
Probability density function of X is cx for x ≥ 0

Solve problems involving random variables, mean, and variance in probability and statistics. This quiz is part of STAT 166: Introduction to Probability and Statistics.