 MAT271 WORKSHEET 1
August 13, 2018
Question 1 (a) In how many dierent ways can the word REARRANGE be rearranged?
(b) How many committees of 2 men and 3 women can be chosen from a group of 6 men and 4 women? Ans: 60, Use combinations.
(c) Suppose there are 11 batteries on a shelf, 4 are defective and 7 non-defective. If 3 are chosen at random, how many distinct ways can
(i). any 3 be chosen? Ans: 11 C3
(ii). no defective be chosen? Ans: 35
(iii). 1 defective and 2 non defective be chosen? Ans: 84. Hence what is the probability of choosing 1 defective and 2 non defective? Ans: (4 C1 7C 2) =11 C3.
Question 2 (a) You have to throw 3 dice in a special game. If it’s known that you need 15 or higher in this
throw to win then what’s the chance of winning this game? Ans: Total no. of cases= 216, and
favorable cases= 20 so that probability of winning is 20 216
=5 54
.
(b) What is the probability of choosing 2 red balls from an urn that has 6 red balls, 5 blue balls and 2 green balls in it? Ans: 5 =26 Use Combinations or Hypergeometric Distr.
Question 3 (a) (i). Dene a probability mass function(PMF) and prove that
f(x ) = 2
x +1 25
,
x = 0 ;1 ;2 ;3 ;4 is
a PMF.
(ii). Given pdf f(x ) =
2; 0 x 1 2
0 ; otherwise
5
nd P(0 :42 < X < 0:49).
(iii). Dene the CDF for a continuous r.v. then nd the CDF of the pdf in (ii) above.
(b) (i). Given f(x ) =
k(4 x2
); 2 < x < 2
0 ; elsewhere
if f(x ) is a PDF nd k. 5
(ii). Find EX and V ar(X ) for the PDF in (ii).
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