11. Let X denote the number of times a certain numerical control machine will ma

Question

11. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as f(x,y) 1 0.05 0.05 0.10 0.05 0.100.35 0.00 0.20 0.10 a. Verify that f(x, y) is a valid probability distribution. b. Find the marginal pmf of X c. Find the marginal pmf of Y d. Find the condition pmf of X given Y = 3, that is, f(x13), and then calculate E(xy-3). e. Find the condition pmf of Y given X = 3, that is, fol 3). f. Calculate P(1 S Y

Explanation / Answer

a)

f(x,y) is a probbility distribution, if sum sum (F(x,y)) = 1

and each f(x,y) has value between [0, 1]

here, sum sum(f(x,y))= 1 as obsevred form table

hence, f(x,y) is a probability distribution

b)

marginal of X

c)

marginal of Y

d)

x y 1 2 3 sum 1 0.05 0.05 0.1 0.2 3 0.05 0.1 0.35 0.5 5 0 0.2 0.1 0.3 sum 0.1 0.35 0.55 1

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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