The following is the c.d.f. of r.v. X x -3 -2 -1 0 1 2 3 4 F(X) 0.1 0.3 0.5 0.65 0.75 0.85 0.9 1 P (X ≤ 3/ X > 0) - Mathematics and Statistics

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Theorem

The following is the c.d.f. of r.v. X

x -3 -2 -1 0 1 2 3 4
F(X) 0.1 0.3 0.5 0.65 0.75 0.85 0.9

1

P (X ≤ 3/ X > 0)

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Solution

(X ≤ 3) ∩ (X > 0)

= {-3, -2, -1, 0, 1, 2, 3} ∩ {1, 2, 3, 4}

= {1, 2, 3}

∴ P[(X ≤ 3) ∩ ( X > 0)]

= P(X = 1)+ P(X = 2)+ P(X = 3)

∴ P[(X ≤ 3) / ( X > 0)]

= `(P[(X ≤ 3) ∩ ( X > 0)])/(P(X > 0))`

= `(P(X = 1)  +  P(X = 2)  +  P(X=3))/(P(X = 1) + P(X = 2)  +  P(X = 3) + P(X = 4))`

= `(0.1 + 0.1 + 0.05)/(0.1 + 0.1 + 0.05 + 0.1)`

=`0.25/0.35`

= `5/7`

Concept: Probability Distribution of Discrete Random Variables
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Chapter 7: Probability Distributions - Miscellaneous Exercise 2 [Page 244]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Miscellaneous Exercise 2 | Q 9.3 | Page 244

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