The random variable X Ā  has a probability distribution P ( X ) of the following form, whereĀ  ' 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

[Class 12 SQP] The random variable X has probability distribution P(X) - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 27 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
part 3 - Question 27 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12 part 4 - Question 27 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

Ā 

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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 = šŸ/šŸ” Our probability distribution table is P(X < 2) = P(X = 0) + P(X = 1) = k + 2k = 3k = 3 Ɨ šŸ/šŸ” = šŸ/šŸ (iii) Find P (X > 2) Given š‘ƒ(š‘‹)={ā– (š‘˜," if " š‘„=0@2š‘˜," if " š‘„=1@3š‘˜," if " š‘„=2@ā–ˆ(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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