CBSE Class 12 Sample Paper for 2024 Boards

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Question 27 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by

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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Transcript

(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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