Probability distribution

Chapter 13 Class 12 Probability (Term 2)
Concept wise

### 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) = {β(0.1 , ππ π₯=0@ππ₯, ππ π₯=1 ππ 2@π(5βπ₯), ππ π₯=3 ππ 4@0, ππ‘βπππ€ππ π)β€ (a) Find the value of kMaking in tabular foArmat Since X is a random variable , its Sum of Probabilities is equal to 1 β_0^4βγπ(π)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 β 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 β€ 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