Question:

1) Indicate whether or not the following Chi-square statistics are significant:

a) 2.75; k =2__________

b) 11.00; k =5__________

c) 12.40; df = 6 __________

1.2) A social worker has been asked to testify before her state legislature about the impact of long-term foster care on child outcomes and government spending. She knows that 60% of children who remained in the foster care system without being adopted ended up in prison. The figure for foster care children who were eventually adopted was 25%. These data were based on 500 children who remained in foster care and 800 children who were eventually adopted. Calculate and interpret Chi-square.

1.3) Calculate and interpret the z score based on the proportion of youth who end up in prison using the data from the previous example.

4.1 Two Types of Random Variables 4.2. Probability Distributions for Discrete Random Variables 1. What is a random variable? 2. Give examples for discrete random variable, continuous random variableProblem 2: 2.1) Write down the mathematical definition of each of the following. (Be precise in your definitions. Each definition should be a mathematical statement.) (a) A random variable (b) The pdf of a random variable. (Specify whether the random variable is discrete or continuous.) (c) The pmf of a random variable. (Specify whether the random variable is discrete or continuous.) (d) The cdf of a random variable. (Specify whether there are any restrictions on whether the random variable is discrete or continuous.) (e) the expected value of a random variable. (Give separate expressions for discrete and continuous random variables.) (f) the expected value of a function of a random variable. (Give separate expressions for discrete and continuous random variables.) 2.2) Write down the mathematical definition of each of the following random variables. (Each definition should be a mathematical statement.) For any parameters of the distribution, explain the meaning of each parameter. Specify whether each of these is a discrete or continuous random variable. (a) a Bernoulli random variable (b) a Binomial random variable (c) a geometric random variable (d) a Poisson random variable (e) a uniform random variable (f) an exponential random variable (g) a normal (or Gaussian) random variableDetermine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. Is the amount of rainfall in a month is a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. b. Is the list of books listed for a book club event a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. c. Is the number of cars a dealership owns a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continous random variable. O C. It is not a random variable.