Solve the following problem : The probability distribution of a discrete r.v. X is as follows.Find P(X ≤ 4), P(2 < X < 4), P(X ≤ 3). - Mathematics and Statistics

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Solve the following problem :

The probability distribution of a discrete r.v. X is as follows.

X 1 2 3 4 5 6
(X = x) k 2k 3k 4k 5k 6k

Find P(X ≤ 4), P(2 < X < 4), P(X ≤ 3).

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Solution

a. P(X ≤ 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= k + 2k + 3k + 4k
= 10k
= `(10)/(21)`

b. P(2 < X < 4) = P(X = 3) = 3k = `(3)/(21) = (1)/(7)`

c. P(X ≥ 3) = 1 – P(X < 3)
= 1 – [P(X = 1) + P(X = 2)]
= 1 – (k + 2k) = 1 – 3k
= `1 - (3)/(21)`

= `1 - (1)/(7)`

=`(6)/(7)`.

Concept: Probability Distribution of Discrete Random Variables
  Is there an error in this question or solution?
Chapter 8: Probability Distributions - Part I [Page 155]

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