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exercises and exams , solutions for mathematics for Economics, Exams of Mathematics for Computing

Atlantic Union College (AUC)Mathematics for Computing

exercises and exams , solutions for mathematics for Economics

Typology: Exams

2020/2021

Uploaded on 06/23/2023

mostafa-allam
mostafa-allam ๐Ÿ‡บ๐Ÿ‡ธ

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Quantitative Methods 1b Formula sheet
Probability
Distributions
Sampling
Confidence Intervals
Hypothesis Tests
๐‘‰๐‘Ž๐‘Ÿ(๐‘‹)=๐ธ(๐‘‹2)โˆ’[๐ธ(๐‘‹)]2
๐‘ƒ(๐ต|๐ด)=๐‘ƒ(๐ด๐‘Ž๐‘›๐‘‘๐ต)
๐‘ƒ(๐ด)
๐‘ƒ(๐ด|๐‘‹)=๐‘ƒ(๐‘‹|๐ด)๐‘ƒ(๐ด)
๐‘ƒ(๐‘‹|๐ด)๐‘ƒ(๐ด)+๐‘ƒ(๐‘‹|๐ต)๐‘ƒ(๐ต)
๐ถ๐‘œ๐‘ฃ(๐‘‹,๐‘Œ)=๐ธ(๐‘‹๐‘Œ)โˆ’๐ธ(๐‘‹)๐ธ(๐‘Œ)
๐‘‹~๐ต๐‘–๐‘›(๐‘›,๐‘)โ†’๐‘ƒ(๐‘‹=๐‘ฅ)=๐‘๐‘ฅร—(1โˆ’๐‘)๐‘›โˆ’๐‘ฅ ร—๐‘›๐ถ๐‘ฅ
๐‘‹~๐‘ƒ๐‘œ๐‘–(๐œ‡)โ†’๐‘ƒ(๐‘‹=๐‘ฅ)=๐œ‡๐‘ฅ๐‘’โˆ’๐œ‡
๐‘ฅ!
๐‘‹~๐‘(๐œ‡,๐œŽ2)โ†’๐‘ง=๐‘ฅโˆ’๐œ‡
๐œŽ
๐‘ง=๐‘ฅ๎ชงโˆ’๐œ‡
๐œŽ
โˆš๐‘›
๐‘ˆ=๐‘ฅ๎ชง+๐‘ง๐›ผ/2 ๐œŽ
โˆš๐‘›
๐ฟ=๐‘ฅ๎ชงโˆ’๐‘ง๐›ผ/2 ๐œŽ
โˆš๐‘›
๐‘ˆ=๐‘ฅ๎ชง+๐‘ง๐›ผ/2โˆš๐‘ฅ๎ชง(1โˆ’๐‘ฅ)
๏Œค
๏Œค
๏Œค
๐‘›
๐ฟ=๐‘ฅ๎ชงโˆ’๐‘ง๐›ผ/2โˆš๐‘ฅ๎ชง(1โˆ’๐‘ฅ)
๏Œค
๏Œค
๏Œค
๐‘›
๐‘ˆ=๐‘ฅ๎ชง+๐‘ก๐›ผ/2,๐‘›โˆ’1 ๐‘ 
โˆš๐‘›
๐ฟ=๐‘ฅ๎ชงโˆ’๐‘ก๐›ผ/2,๐‘›โˆ’1 ๐‘ 
โˆš๐‘›
๐‘ง=๐‘ฅ๎ชงโˆ’๐œ‡0
๐œŽ
โˆš๐‘›
๐‘ง= ๐‘ฅ๎ชงโˆ’๐œ‡0
โˆš๐œ‡0(1โˆ’๐œ‡0)
๐‘›
๐‘ก=๐‘ฅ๎ชงโˆ’๐œ‡0
๐‘ 
โˆš๐‘›
๐ธ(๐‘Ž+๐‘๐‘‹)=๐‘Ž+๐‘๐ธ(๐‘‹)
๐‘‰๐‘Ž๐‘Ÿ(๐‘Ž+๐‘๐‘‹)=๐‘2๐‘‰๐‘Ž๐‘Ÿ(๐‘‹)

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Quantitative Methods 1b Formula sheet

Probability

Distributions

Sampling

Confidence Intervals

Hypothesis Tests

2

) โˆ’ [๐ธ(๐‘‹)]

2

๐‘ฅ

ร— ( 1 โˆ’ ๐‘)

๐‘›โˆ’๐‘ฅ

ร— ๐‘›๐ถ๐‘ฅ

๐‘ฅ

โˆ’๐œ‡

2

2

๐›ผ/ 2

๐›ผ/ 2

๐›ผ/ 2

๐›ผ/ 2

๐›ผ/ 2 ,๐‘›โˆ’ 1

๐›ผ/ 2 ,๐‘›โˆ’ 1

0

0

0

0

0

2