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1 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi for a. r> 0 and 0 << 271 p < 0 and 0 < < 271 )
Find the area under the graph of g over [-2, 3] g(x) = -x? +5 when x 50 g(x) = x + 5 when x > 0
A= 10 5 5 2 B= 4. 1 > ,A+B= . ] 0
2. Suppose Xi ~ N(8,02) where θ > 0. (a) Show that s--(x, Σ¡! xi) is a sufficient statistic of θ where X is the sample mean. (b) Is S minimal sufficient? (c) Can you find a non-constant function g(.) such that g(S) is an ancillary statistic?
(b) Find an example of an open set G in a metric space X and a closed subset F of G such that there is no δ > 0 with {x : dist(x, F) < δ} C G
The cumulative distribution function of the random variable X is given by F(x) = 1-e-r' (z > 0). Evaluate a) P(X > 2) b) P(l < X < 3 c) P(-1 〈 X <-3). d) P(-1< X <3)
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
(5) Let X, i = 1,...,n be iid sample from density fx(x) = f(x) e-/201(x > 0), 4 > 0 V TO (a) Find k. (b) Find E(X). (c) Find Var(X). (d) Find the MLE for 0. (e) Find MOM estimator for A. (f) Find bias for MLE. (g) Find MSE of MLE. (h) Let Y = x, find probability density function of Y. (i) Let Y = X?, find cumulative distribution function of Y. 5
Enthalpy of Formation Part 1: Part 2: Part 3: A scientist measures the standard enthalpy change for the following reaction to be 591.0 kJ : 2H2O(1)—>2H2(g) + O2(g) Based on this value and the standard enthalpies of formation for the other substances, the standard enthalpy of formation of H2O(l) is kJ/mol. A scientist measures the standard enthalpy change for the following reaction to be -2903.4 kJ: 2C2H6(g) + 7 O2(g)—>4CO2(g) + 6 H2O(g) Based on this value and the standard...