Question

A random variable is uniformly distributed between 100 and 150. a. Draw the density function. b. Find P(X > 110). c. Find P(120 < X < 135). d. Find P(X < 122).

Answer 1

$f(x) = \dfrac{1}{b-a} = \dfrac{1}{50}$

a.) Probability density function can be drawn as,

b.) P(X > 110)

$= (150-110)\dfrac{1}{50}$

$= \dfrac{4}{5}$

$= 0.8$

c.) P(120 < X < 135)

$= (135-120)\dfrac{1}{50}$

$= \dfrac{15}{20}$

$= 0.3$

d.) P(X < 122)

$= (122-110)\dfrac{1}{50}$

$= 0.24$