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The random variable X   has a probability distribution P ( X ) of the following form, where  ' k ' is some real number:

P(X) = {k , if x = 0, 2k , if x = 1, 3k , if x = 2, 0 otherwise

(i) Determine the value of k.

(ii) Find P (X<2)

(iii)Find P (X>2)

This question is similar to Question 9 Chapter 13 Class 12

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(i) Find k Since X is a random variable , its Sum of Probabilities is equal to 1 P(X = 0) + P(X = 1) + P(X = 2) = 1 k + 2k + 3k = 1 6k = 1 k = 𝟏/𝟔 Our probability distribution table is P(X < 2) = P(X = 0) + P(X = 1) = k + 2k = 3k = 3 × 𝟏/𝟔 = 𝟏/𝟐 (iii) Find P (X > 2) Given 𝑃(𝑋)={■(𝑘," if " 𝑥=0@2𝑘," if " 𝑥=1@3𝑘," if " 𝑥=2@█(0," otherwise" @" " ))┤ For value of X other than 0, 1 and 2, the P(X) = 0 P(X > 2) = P(X = 3) + P(X = 4) + …… = 0 + 0 + ….. = 0

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.