Question

can someone solve question 8?

WRITTEN HOMEWORK A e. Find Var(14x). eroblem 8: An emer gency medical clinic has two work centers: the first checks in and examines the patient and the second center treats the patient. Let X and Y behe drtdon variabies reperesemtingche mber of minutes in the first and second work centers, respect vely. Assume X and Y are independent. (2 points) E(X): 18.1, σχ-8.2 E(Y) 30.5, ơr 15.2 a. Let W X+Y be the random variable representing the treat a patient. Compute the mean, variance, and standard deviation of W Suppose there is a flat rate of $25 for the examination, and a per minute charge of $1.10 to treat the patient. Let the charge C = 1.1Y + 25, Compute the mean, variance, and standard deviation of C.

Answer 1

a) $E[W]=E[X+Y]=E[X]+E[Y]=18.1+30.5=48.6$

$Var[W]=Var[X+Y]=Var[X]+Var[Y]+2Cov(X,Y)=(8.2)^2+(15.2)^2+0=298.28$

$Standard.deviation[W]=\sqrt{298.28}=17.27$

b) Mean = $E[C]=1.1E[Y]+25=1.1*30.5+25=58.55$

variance $Var[C]=(1.1)^2Var[Y]=(1.1)^2(15.2)^2=279.56$

standard deviation of C = $\sqrt{279.56}=16.72$