The annual number of claims from a particular risk has a Poisson distribution with mean /. The prior distribution for / has a gamma distribution with o =2 and 1 =5. Claim numbers M. .... x, over the last n years have been recorded. (i) Show that the posterior distribution is gamma and determine its parameters. [3] (ii) Given that n = 8 and ) x; =5 determine the Bayesian estimate for // under: i=1 (a) squared-error loss (b) "all-or-nothing" loss (c) absolute error loss. [5] [Total X]The annual number of claims from a particular risk has a Poisson distribution with mean /. The prior distribution for / has a gamma distribution with o =2 and 1 =5. Claim numbers M. .... x, over the last n years have been recorded. (i) Show that the posterior distribution is gamma and determine its parameters. [3] (ii) Given that n = 8 and ) x; =5 determine the Bayesian estimate for // under: i=1 (a) squared-error loss (b) "all-or-nothing" loss (c) absolute error loss. [5] [Total X]11. (18 Points) Consider a market with two horizontally differentiated firms, X and Y. Each has a constant marginal cost of $20. Demand functions are Qx = 100 - 2Px + Py Qy = 100 - 2Py + Px a) (10 Points) Calculate the Bertrand equilibrium in prices in this market. b) (8 Points) Draw the best response function diagram corresponding to your solution.1. The table on the right contains employment data for males and females between May 2020 and April 2021. The data is seasonally adjusted and comes from the Labour Force Survey for Canada as a whole. Employment a) What is the significance of the data being "seasonally Males Females adjusted"? How can we compare the data because of this May-20 8,800.50 7,643.40 Jun-20 9,277.00 8,108.70 trait? Jul-20 9,441.20 8,361.40 b) Create a time series graph using this data. Aug-20 9,519.40 8,496.90 c) Explain what the data shows in terms of trend for both Sep-20 9,688.70 8,699.90 Oct-20 9,742.90 8,740.10 males and females over the year. Nov-20 9,775.00 8,762.40 d) Does the relative size of employment change for one Dec-20 9,752.10 8,732.70 gender vs. the other? Jan-21 9,674.00 8,598.00 e) What other aspects of employment might be useful when Feb-21 9,797.60 8,733.60 Mar-21 9,951.60 8,882.70 comparing male and female employment? Apr-21 9,869.20 8,758.00A random sample of 100 claim amounts M,x,...., Mon is observed from a Weibull distribution with parameter y = 2, where a is unknown. For these data: Er, = 487, 926 Ex- = 976,444,000 median = 4,500 (i) (a) Show that the maximum likelihood estimator for c is given by: 8 =n (b) Hence estimate the value of c. [4] (ii) Estimate the value of e using the method of moments. (2] (iii) Calculate the method of percentiles estimate of c. [2] [Total 8]A random sample of 100 claim amounts M,x,...., Mon is observed from a Weibull distribution with parameter y = 2, where a is unknown. For these data: Er, = 487, 926 Ex- = 976,444,000 median = 4,500 (i) (a) Show that the maximum likelihood estimator for c is given by: 8 =n (b) Hence estimate the value of c. [4] (ii) Estimate the value of e using the method of moments. (2] (iii) Calculate the method of percentiles estimate of c. [2] [Total 8]4) What makes a secondary source "academic" or "scholarly" such that you could actually use it in a research essay? See pp. 1956-1957. 5) Whenever you want to summarize, paraphrase, or quote from a secondary source, you must introduce that source. Apply the methods discussed on pp. 1960-1961 to the following and introduce this as a source in an imaginary essay. Author of Article: Keith Byerman Title of Article: "Anger in a Small Place: Jamaica Kincaid's Cultural Critique of Antigua" Argument of Article: In exploring Jamaica Kincaid's corpus of works, it is quite obvious that she confronts the problems that colonialism has created on the island of Antigua. What may be less apparent is that her writing also challenges traditional Antiguan culture and does so in gendered terms: she examines and critiques the social effects of sharply divided gender roles