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Continuous random variables and the normal distribution — Question 336

Original QCE Vault practice · 8 marks

Q336 · Practice questionTechnology-freeComplex unfamiliar8 marks

QUESTION 336 (8 marks)

A waiting-time model has density

f_a(x)=\dfrac{ae^{-ax}}{1-e^{-2a}}

for

0\leq x\leq2

, and zero otherwise, where

a>0

. Measurements indicate that

P(X\leq1)=3/4

.

Decreasing truncated exponential waiting-time density on [0,2], zero outside its support.

a)

Verify that the density integrates to

1

for every

a>0

.

[2 marks]

b)

Determine

a

exactly.

[3 marks]

c)

For this value of

a

, determine the exact median.

[3 marks]

Question linkSyllabus coverage

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