Jay plans to open a new restaurant in River City. Of course, he will have to fil

Question

Jay plans to open a new restaurant in River City. Of course, he will have to fill out forms for different agencies. In particular he is worried about the health department forms and the garbage department forms. The number of these forms is uncertain but he knows that there will be between 3 and 5 health department forms and between 1 and 3 garbage department forms. Let X = the number of health department forms and Y = the number of garbage department forms which he must fill out. Let Z = X + Y. The following is the joint probability mass function for X and Y:

a. What is the probability that Z > 4?
b. What is the probability X = 3?
c. What is the probability Y = 2?
d. Calculate the expected number of health department forms to be filled out.
e. Calculate the expected number of garbage department forms to be filled out.
f. Calculate the covariance of X and Y.
g. Calculate the correlation coefficient between X and Y.
h. What is the probability that X=4 given Y = 2?
i. What is the expected value of 8X - 7Y?

1 2 3 3 .16 .14 .05 4 .10 .20 .05 5 .10 .10 .10

Explanation / Answer

a)P(Z>4) =1-P(X=3,Y=1) =1-0.16=0.84

b)P(X=3)=0.16+0.14+0.05=0.35

c) P(Y=2) =0.14+0.2+0.1 =0.44

d) from above E(X)=3.95

e) E(Y) =1.84

f) for E(XY) =7.37

hence Covariance =E(XY)-E(X)E(Y) =0.102

g) correlation coefficient =Covar(X,Y)/(Var(X)*Var(Y))1/2 =0.1734

h) P(X=4|Y=2)=0.2/0.44 =0.4545

i) E(8X-7Y)=8E(X)-7*E(Y) =18.72

x P(x) xP(x) x^2P(X) 3 0.35 1.05 3.15 4 0.35 1.4 5.6 5 0.3 1.5 7.5 total 1 3.95 16.25 E(X) = 3.95 E(X^2) = 16.25 Var(X) =E(X^2)-((EX))^2 0.6475 y P(y) yP(y) y^2P(y) 1 0.36 0.36 0.36 2 0.44 0.88 1.76 3 0.2 0.6 1.8 total 1 1.84 3.92 E(Y) = 1.84 E(Y^2) = 3.92 Var(Y) =E(Y^2)-((EY))^2 0.5344

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.