Assume that Y1, ..., Yn are IID normal random variables with mean 0 and variance σ 2 . Thus, the PDF for any Yi is given by: p(y|σ 2 ) = 1 √ 2πσ exp [− y 2 2σ 2 ]. A conjugate prior for σ 2 is an inverse-gamma distribution. That is, an inverse-gamma distribution with parameters α and β is given by: p(σ 2 ) = β α Γ(α) (1/σ2 ) α+1 exp [−β/σ2 ]. (Note that σ 2 > 0.) Complete the following: • Derive the posterior distribution for σ 2 assuming n IID normal data points in a sample and an inversegamma prior, as above. You should find that the posterior distribution is also an inverse-gamma distribution. What are the parameters of

For a field trip to the zoo, 4 students rode in cars and the rest filled nine busess. how many students were in each bus if 472 students were on the trip

You are saving to buy a bicycle; so far you save 55.00. the bicycle costs 199.00. you earn 9.00 per hour at your job. which inequality represents the possible number of h hours you need to work to buy the bicycle?

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.