Question Solved1 Answer Task 1 1. An analog signal contains frequencies upto 10 kHz. This signal is sampled at 50 kHz. Design an FIR filter using windowing technique for a transition band of 5 kHz. The filter should provide minimum –21 dB attenuation at the end of transition band. Task 1 1. An analog signal contains frequencies upto 10 kHz. This signal is sampled at 50 kHz. Design an FIR filter using windowing technique for a transition band of 5 kHz. The filter should provide minimum –21 dB attenuation at the end of transition band.

(1) Let X [X1, X2, X3]' be a random vector with joint probability density function defined by 6, 0 <I1 <12 <13 <1 f(x1, x2 x 3) = 0, elsewhere Find the conditional distribution of X1, X2 given X3 = x (2) Let X1, X2, X3, X4 have the joint probability density function f(x1, x2, x3, x4) = { 24e-(11+12+13+14), 0 < x1, 12, 13, 14 < 0 0, elsewhere Let Y1 = X1,Y, = X2 – X1,Y3 = X3 – X2,YA = X4 - X3. (i) Using the change of variable technique, find the joint probability density function of Y1, Y2, Y3, YA (ii) Find the conditional distribution of Y4 given Yı, Y2, Y3 (3) Let X1, X2, ..., X, be a random sample from population having probability density func- tion 1 f(xi) e-(232(1:-u)), - <2 < 0 = ce V2πσ2 (i) Using the characteristic function technique, determine the distribution of n2 Y = ΣΧ? i=1 (ii) Using the moment generating function technique, determine the distribution of the sample mean X (4) Let X1, X2, ...Xn be a random sample from population having normal distribution with mean p and variance o2. Let X and Sº be the sample mean and sample variance respectively. Find the joint distribution of X and S.

Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 0-3 5 -4 4-10 0 0 4 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (A1, A2, A3)= a basis for each of the corresponding eigenspaces X₁ = X3 = Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 0-3 5 -4 4-10 0 0 4 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (A1, A2, A3)= a basis for each of the corresponding eigenspaces X₁ = X3 =

4. Measuring GDP The following table shows data on consumption, investments, exports, imports, and government expenditures for the United States in 2018, as published by the Bureau of Economic Analysis. All figures are in billions of dollars. Fill in the missing cells in the table to calculate GDP using the expenditure approach. Data (Billions of dollars) 4. Measuring GDP The following table shows data on consumption, investments, exports, imports, and government expenditures for the United States in 2018, as published by the Bureau of Economic Analysis. All figures are in billions of dollars. Fill in the missing cells in the table to calculate GDP using the expenditure approach. Data (Billions of dollars) Consumption (C) 13,948.5 Investment (1) 3,650.1 Exports (X) 2,531.3 Imports (M) 3,156.7 Net Exports of Goods and Services Government Purchases (G) 3.520.8 Gross Domestic Product (GDP) 4

2 . Real versus nominal GDP Consider a simple economy that produces two goods: beers and paper plates. The following table shows the prices and quantities of the goods over a three-year period. Year Beers Paper plates Price Quantity Price Quantity (Dollars per beer) (Number of beers) (Dollars per paper plate) (Number of paper plates) 2018 2 265 1 160 2019 2 135 4 230 2020 2 135 4 180 Use the information from the preceding table to fill in the following table. Year Nominal GDP Real GDP GDP Deflator (Dollars) (Base year 2018, dollars) 2018       2019       2020       From 2019 to 2020, nominal GDP    , and real GDP    . The inflation rate in 2020 was    . Why is real GDP a more accurate measure of an economy's production than nominal GDP? Real GDP measures the value of the goods and services an economy produces, but nominal GDP measures the value of the goods and services an economy consumes. Real GDP is not influenced by price changes, but nominal GDP is. Real GDP includes the value of exports, but nominal GDP does not.

For Chesapeake Limited’s statement of financial position, indicate the proper classification for the following items: Question 5 of 7 -/1 View Policies Current Attempt in Progress For Chesapeake Limited's statement of financial position, indicate the proper classification for the following items: Classification Account (a) Preferred Shares (b) Franchises (c) Salaries and Wages Payable (d) Accounts Payable Leasehold Improvements Contributed Surplus Current Assets Accumulated Other Comprehensive Income Capital Shares Other Assets Current Liabilities Retained Earnings Intangible Assets Long-Term Debt Long-term Investments Property. Plant, and Equipment (e) (f) FV-NI Investments g) (h) (0) Current Portion of Long-Term Debt Obligations under Lease (portion due next year) Allowance for Doubtful Accounts Accounts Receivable Bonds Payable (maturing in two years) Notes Payable (due next year) c) (k) (1) (m) Supplies (n) Mortgage Payable (principal portion due beyond next year) (0) Land (for use) (p) Bond Sinking Fund Investment (9) Inventory (r) (s) Prepaid Insurance Bonds Payable (maturing next year) Income Tax Payable (t) (u) Unrealized Gain or Loss-OCI (v) Defi

Solve the following Bernoulli equations: a) x2y' + 2y = 2e1/xy1/2 answer: y = e2/x(c-1/x)2 b) xy' + y = x4y4 y(1) = 1/2 answer: y = 1/x(11-3x)1/3