1. For the following problems, identify all possible combina- tions of the two c
ID: 3351509 • Letter: 1
Question
1. For the following problems, identify all possible combina- tions of the two categorical variables. (a) Grade (A, B, C, D, F) and employment status (Uncm- ployed (U), Employed at least part time (F)). (b) Cancer status (has cancer, or does not), and age group (Young, Middle. Old). (c) Smoking status (Smoker, Non-smoker), and illegal drug activity (Recently used, Used in the past, Never used (d) Intelligence of dog (high, medium, low). and type of dog (Border Collie, German Shepard, Dachshund). 2. Assume that Y is a randon variable with mean tly = 4, and standard deviation Y = 8, Find the mean and stan- dard deviations for the following random variables: (a) U1=344Y (b) U2=-10+2Y (c) U3 = 1/4-Y (d) U4= 3/4-(1/4)YExplanation / Answer
a)possible combinations ={(A,U),(B,U),(C,U),(D,U),(F,U),(E,U),(E,U),(E,U),(E,U),(E,U)}
b)possible combinations ={(has cancer,Young),(has cancer,middle),(has cancer,old),(doe not ,Young),(doe not,middle),(doe not,old)}
c)possible combinations ={(smoker; recently used),(smoker; used in the past),(smoker; never used),
(non-smoker; recently used),(non-smoker; used in the past),(non-smoker; never used)}
d)
possible combinations ={(high,Border Collie),(high,German Shephard),(high,Dachshund),(medium,Border Collie),(medium,German Shephard),(medium,Dachshund),(low,Border Collie),(low,German Shephard),(low,Dachshund))
2)
mean =3+4E(Y) =3+4*4=19
std deviation =4*SD(Y)=4*8=32
b) mean =-10+2E(Y)=-10+2*4=-2
std deviation =2*SD(Y)=2*8=16
c)mean =1/4-E(Y) =1/4-4 =-15/4
std deviation = SD(Y) =8
d) mean =(3/4)-(1/4)E(Y)=(3/4)-(1/4)*4=-1/4
std deviation =(1/4)*SD(Y)=(1/4)*8=2
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