Suppose the random variables X1, X2, and, X are mutually independent and represe

Question

Suppose the random variables X1, X2, and, X are mutually independent and represent the time it takes to gather ingredients, prepare/cook the ingredients, and assemble the ingredients, respectively. The total meal preparation time is thus Y-Xi+ X2 + X3. X1 is normally distributed with mean 8 and standard deviation 2. X2 is normally distributed with mean 12 and standard deviation 2. X3 is normally distributed with mean 4 and standard deviation 1. a. What is the distribution of Y:? multivariate normal geometric multinomial normal exponential negative multinomial Poisson Submit Answer Tries 0/10 Round all answers to 4 decimal points. b. Find E(Y) Submit Answer Tries 0/5 c. Find Var(Xi + X2). Submit Answer Tries 0/5

Explanation / Answer

a) normal

b) E(Y)=E(X1)+E(X2)+E(X3)=8+12+4=24

c)Var(X1+X2)=Var(X1)+Var(X2)=22+22 =8

d)Var(Y)=Var(X1)+Var(X2)+Var(X3)=22+22 +12 =9

e) std deviation of Y SD(Y)=(9)1/2 =3

P(Y<27)=P(Z<(27-24)/3)=P(Y<1) =0.8413

f) P(Y>18)=P(Z>(18-24)/3)= P(Z>-2) =0.9772

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