# Example 26

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Example 26 Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant. P(X = x) = 0.1 , ๐๐ ๐ฅ=0๏ทฎ๐๐ฅ, ๐๐ ๐ฅ=1 ๐๐ 2๏ทฎ๐ 5โ๐ฅ๏ทฏ, ๐๐ ๐ฅ=3 ๐๐ 4๏ทฎ0, ๐๐กโ๐๐๐ค๐๐ ๐๏ทฏ๏ทฏ (a) Find the value of k Making in tabular format Since X is a random variable , its Sum of Probabilities is equal to 1 0๏ทฎ4๏ทฎ๐(๐)๏ทฏ = 1 P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1 0.1 + k + 2k + 2k + k = 1 6k = 1 โ 0.1 6k = 0.9 k = 0. 9๏ทฎ6๏ทฏ k = 0.15 Example 26 (b) What is the probability that you study atleast two hours? Exactly two hours? At most 2 Hours Our probability distribution table is P(you study atleast two hours) = P(X โฅ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 2k + 2k + k = 5k = 5 ร 0.15 = 0.75 P(you study exactly two hours) = P(X = 2) = 2k = 2 ร 0.15 = 0.30 P(you study atmost two hours) = P(X โค 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + k + 2k = 0.1 + 3k = 0.1 + 3 ร 0.15 = 0.1 + 0.45 = 0.55

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Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.