Homework #2

You can also get the PDF format of Wenqiang’s Homework.

Q1

• 1. \(n=10, \pi=0.2, y=3\)

P = dbinom(3, 10, 0.2)
P

## [1] 0.2013266

• 2. \(n=4, \pi=0.4, y=2\)

P = dbinom(2, 4, 0.4)
P

## [1] 0.3456

• 3. \(n=16, \pi=0.7, y=12\)

P = dbinom(12, 16, 0.7)
P

## [1] 0.2040483

Q2

• 1. \(P(y\leq4)\)

P = pbinom(4, 8, 0.4)
P

## [1] 0.8263296

• 2. \(P(y>4) = 1 - P(y\leq4)\)

P = 1 - pbinom(4, 8, 0.4)
P

## [1] 0.1736704

• 3. \(P(y\leq7) = P(y\leq7) - P(y=7)\)

P = pbinom(7, 8, 0.4) - dbinom(7, 8, 0.4)
P

## [1] 0.9914803

• 4. \(P(y\geq6) = 1 - P(y\leq6) + P(y=6)\)

P = 1 - pbinom(6, 8, 0.4) + dbinom(6, 8, 0.4)
P

## [1] 0.04980736

Q3 Exercise 4.46

• 1. two are rated as outstanding
  • P(outstanding) = 0.1
  • P(X=2) = dbinom(2, 10, 0.1) = 0.1937102

dbinom(2, 10, 0.1)

## [1] 0.1937102

• 2. two or more are rated as outstanding
  • P(outstanding) = 0.1
  • \(P(X\geq2) = 1 - P(X\leq1)\) = 1 - pbinom(1, 10, 0.1) = 0.2639011

1 - pbinom(1, 10, 0.1)

## [1] 0.2639011

• 3. eight of the ten are rated either outstanding or excellent
  • P(outstanding or excellent) = 0.1 + 0.75 = 0.85
  • P(X=8) = dbinom(8, 10, 0.85) = 0.2758967

dbinom(8, 10, 0.85)

## [1] 0.2758967

• 4. none of the trainees is rated as unsatisfactory
  • P(unsatisfactory) = 0.05
  • P(X=0) = dbinom(0, 10, 0.05) = 0.5987369

dbinom(0, 10, 0.05)

## [1] 0.5987369