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Continuous random variables and the normal distribution — Question 306

Original QCE Vault practice · 4 marks

Q306 · Practice questionTechnology-freeSimple familiar4 marks

QUESTION 306 (4 marks)

A loading time

X

minutes has cumulative distribution function

F(x)=0

for

x<0

,

F(x)=x^2/9

for

0\leq x\leq3

, and

F(x)=1

for

x>3

.

CDF F(x)=x squared/9 on [0,3], increasing from 0 to 1 and continuing horizontally at 1 to the right of 3.

a)

Determine the density on

0<x<3

.

[1 mark]

b)

Determine

P(1<X<2)

.

[1 mark]

c)

Determine the

90

th percentile exactly.

[2 marks]

Question linkSyllabus coverage

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