21. The amount of bread (in hundreds of pounds) x that a certain bakery is able to sell in a day is found to be a numerical valued random: phenopienon, with a probabiliiy function specified by the p.d.f. (x), given by : k. x for 0 sx< 5 f(x) ={k. (10 – x), for 5

21. The amount of bread (in hundreds of pounds) x that a certain bakery is able to sell in a day is found to be a numerical valued random: phenopienon, with a probabiliiy function specified by the p.d.f. (x), given by : k. x for 0 sx< 5 f(x) ={k. (10 – x), for 5

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.16P

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Question

21. The amount of bread (in hundreds of pounds) x that a certain bakery is
able to sell in a day is found to be a numerical valued random phenomenon, with a probabiliiy
function specified by the p.d.f. f(x), given by :
k. x
={k. (10 – x), for 5 <x < 10
for 0 <x< 5
f (x).
ctherwise
(a) Find the value of k such that f(x) is a provability density function.
(b) What is the probability that the
number of pounds of bread that wil
I be sold tomorrow is: (i) more than
500 pounds, (i) less than 500 poun
ds, and (ii) between 250 and 750 p
ounds ?
(c) Denoting by A, B and C the even
ts that the pounds of bread sold ar
e as in bb (ii) and b (ii) re spectivel
y, find P (AIB), P (A IC). Are (i) A an
d B independent events? (ii) Are A
and C independent events?

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