Question

Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the expected value of X*Y. (i.e. X times Y) g) Find the expected value of 2X - 3Y. h) Find the variance of 2x - 3Y i) Find the expected value of y3 i) Copy your R script for the above into the text box here.

Answer 1

Solution:- from the data, Fonen X 1 3 PCz 0.4 3 PCY) O 3 O-3 O4 Sa Pobability that (x* y-u) PCXY4P (x= 2, yez) =P 60-5). PC=D-3 11 = 0SKO 3 0.15 11 PCx o.15 1 > Expecteol value f x EC)= ERPCx = C1KD4)+ C2eo )+ C3x0-) 0.4 + 1.7 E(x) 1.7

Standard doviation ue Knouw dllat dtandasd deviatoo Varianca .: Variante Cx)- E C)-EC € (x2) ExtpCa 10 (x0.4) +(2x 05)+ (3x o) CIXO 4)4x05)+ (9x01) 11 O.9 O-4 t 2+ - 3. 3 E (x)3-3 Van Cx) 3.3 CI = 3.3-2.89 1 Van Cx)= o4) Standard deuialuon (x) SD Cx)- Joy 2 0.6403 SDCK) O-6403

Gpected alue of Y E CY) EY PCY 3.1 + 11 .. E C)- 3.1T e Standand deuiadion at y Knous that S.D Vasiance ue SD CY)V Vaor Cy) Nan C) E Cy) -CEC ECY EYPCY) (2x 03)+ (3x0-3)+ (4x0-4) x0:3)+ C9 xo3)+ Cl6xD4) 10.3 12+2.+t 6.4 ECY)1o 3 Nan C4 10-3-(3.1 9.61 1D 3 vanC4) 0.69 .. S.D Cy)-Jo.69 S.DCY) O. 83066

f Expectod Vaue ef xy E CxY) E (x) ECY) 11 = 17 x 3- 1 5. 27 E (x *y)- 5.27 Expecteolvalue f 2x-3 y; E C2x-3Y)- 2(K)- 3E(Y) 11 2C.)-3(3-1) 1 3.4-9 3 (2x-3)=5.9 hExpected Nariane 2x - 3y: vasr2x-3y) 2 van C)- 3 Vas Cy) 2 Co.41)-3(0-69) O.82- 2.07 -125 (2x-3y)
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