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Example 26Let X denote the number of hours you study during a randoml

Example 26 - Chapter 13 Class 12 Probability - Part 2
Example 26 - Chapter 13 Class 12 Probability - Part 3 Example 26 - Chapter 13 Class 12 Probability - Part 4


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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) = {β–ˆ(0.1 , 𝑖𝑓 π‘₯[email protected]π‘˜π‘₯, 𝑖𝑓 π‘₯=1 π‘œπ‘Ÿ [email protected]π‘˜(5βˆ’π‘₯), 𝑖𝑓 π‘₯=3 π‘œπ‘Ÿ [email protected], π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’)─ (a) Find the value of kMaking in tabular foArmat Since X is a random variable , its Sum of Probabilities is equal to 1 βˆ‘_0^4▒〖𝑃(𝑋)γ€— = 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 – 0.1 6k = 0.9 k = (0. 9)/6 k = 0.15 Example 26 (b) What is the probability that you study atleast two hours? Exactly two hours? At most 2 HoursOur probability distribution table is P(you study atleast two hours) = P(X β‰₯ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 2k + 2k + k = 5k = 5 Γ— 0.15 = 0.75 P(you study exactly two hours) = P(X = 2) = 2k = 2 Γ— 0.15 = 0.30 P(you study atmost two hours) = P(X ≀ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1 + k + 2k = 0.1 + 3k = 0.1 + 3 Γ— 0.15 = 0.1 + 0.45 = 0.55

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.