## Statistics (12th Edition)

Published by Pearson

# Chapter 5 - Continuous Random Variables - Exercises 5.1 - 5.19 - Applying the Concepts - Basic - Page 230: 5.9a

#### Answer

E(x) = 2. As it is in the middle of 1 and 3, hence the distribution is expected to be uniform.

#### Work Step by Step

f(x) = 1/d-c = 1/3-1 = 1/2 $P(1 \leq x \leq 3) = ∫_{1}^{3} x.f(x).dx$ = $∫_{1}^{3} \frac{1}{d-c}.x.dx$ = $∫_{1}^{3} \frac{1}{2}x..dx$ = $1/2 [x^{2}/2]_{1}^{3}$ = 1/2. [9/2 - 1/2 = 1/2. [8/2] = 2

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