Homework 3 (3.6.1 - 3.6.10)

3.6.1

three yellow and one green?

dbinom(3, size = 4, prob = .75)

## [1] 0.421875

all four yellow?

dbinom(4, size = 4, prob = .75)

## [1] 0.3164063

All four are the same number?

dbinom(0, size = 4, prob = .75)  ## 0 in my understanding is 0 successes to get yellow

## [1] 0.00390625

probability for 4 greens = 0.00390625 probability for 4 yellows = 0.3164063 0.00390625 + 0.3164063 = 0.3203125 = 0.320

3.6.3

44% have type A blood. sample size = 4 p = .44

1. Pr{Y = 0}

dbinom(0, size = 4, prob= .44)

## [1] 0.09834496

2. Pr{Y = 1}

dbinom(1, size = 4, prob= .44)

## [1] 0.3090842

3. Pr{Y = 2}

dbinom(2, size = 4, prob = .44)

## [1] 0.3642778

4. Pr{0 ≤ Y ≤ 2}

0.098 + 0.364 + 0.309 = 0.771

5. Pr{0 < Y ≤ 2}

0.098 + 0.364 + 0.309 = 0.771 (Pr{0 ≤ Y ≤ 2} = Pr{0 < Y < 2} = .771)

3.6.7

p = .08 n = 20

dbinom(0, size = 20, prob = .08)

## [1] 0.1886933

dbinom(1, size = 20, prob = .08)

## [1] 0.3281623

dbinom(2, size = 20, prob = .08)

## [1] 0.2710906

dbinom(3, size = 20, prob = .08)

## [1] 0.1414386

dbinom(4, size = 20, prob = .08)

## [1] 0.05227078

dbinom(5, size = 20, prob = .08)

## [1] 0.01454491

dbinom(6, size = 20, prob = .08)

## [1] 0.003161937

dbinom(7, size = 20, prob = .08)

## [1] 0.0005499022

dbinom(8, size = 20, prob = .08)

## [1] 7.770357e-05

dbinom(9, size = 20, prob = .08)

## [1] 9.009109e-06

dbinom(10, size = 20, prob = .08)

## [1] 8.617409e-07

dbinom(11, size = 20, prob = .08)

## [1] 6.812181e-08

dbinom(12, size = 20, prob = .08)

## [1] 4.442727e-09

dbinom(13, size = 20, prob = .08)

## [1] 2.377379e-10

dbinom(14, size = 20, prob = .08)

## [1] 1.033643e-11

dbinom(15, size = 20, prob = .08)

## [1] 3.59528e-13

dbinom(16, size = 20, prob = .08)

## [1] 9.769782e-15

dbinom(17, size = 20, prob = .08)

## [1] 1.998932e-16

dbinom(18, size = 20, prob = .08)

## [1] 2.897004e-18

dbinom(19, size = 20, prob = .08)

## [1] 2.651719e-20

dbinom(20, size = 20, prob = .08)

## [1] 1.152922e-22

mean = np = (20 .08) = 1.6 standard deviation = sqrt(np(1-p)) = sqrt(1.6(1-0.08)) = 1.213

3.6.10

positive diagnosis in about 70% of cases. 300,000 children to be tested, 8 have the disease

dbinom(8, size = 8, prob = .70)

## [1] 0.05764801

dbinom(7, size = 8, prob = .70)

## [1] 0.1976503

3. Pr{2 or more cases to be missed}=

dbinom(8, size = 8, prob = .70)

## [1] 0.05764801

dbinom(7, size = 8, prob = .70)

## [1] 0.1976503

dbinom(6, size = 8, prob = .70)

## [1] 0.2964755

dbinom(5, size = 8, prob = .70)

## [1] 0.2541218

dbinom(4, size = 8, prob = .70)

## [1] 0.1361367

dbinom(3, size = 8, prob = .70)

## [1] 0.04667544

dbinom(2, size = 8, prob = .70)

## [1] 0.01000188

dbinom(1, size = 8, prob = .70)

## [1] 0.00122472

dbinom(0, size = 8, prob = .70)

## [1] 6.561e-05