1. [14 points] An individual who has automobile insurance from a certain company

Question

1. [14 points] An individual who has automobile insurance from a certain company is randomly selected. Let X = the number of moving violations for which the individual was cited during the last 3 years. The probability mass function of X is given below. p(x) 0.50 0.20 0.15 0.10 0.05 (a) Calculate the probability of each of the following events. [2 points each] (i) Exactly one moving violation (ii) At most one moving violation (iii) More than two moving violations (iv) Between 1 and 3 (inclusive of the endpoints) moving violations (b) Find the cumulative distribution function F(x). Be sure to write your answer in the appropriate way. [6 points] 2. [6 points] Suppose that two fair, six-sided dice are rolled independently of each other. For each possible roll define X = the smaller of the two dice. Find the probability mass function of X. Write your answer using a table similar to that given in Problem 1 .

Explanation / Answer

Ans:

a)

i)P(1)=0.2

ii)P(x<=1)=P(0)+P(1)=0.5+0.2=0.7

iii)P(x>2)=P(3)+P(4)=0.1+0.05=0.15

iv)P(1<=x<=3)=P(1)+P(2)+P(3)=0.2+0.15+0.1=0.45

b)

2)Sample space for 2 dice roll:

Probability mass function of X:

x 0 1 2 3 4 p(x) 0.5 0.2 0.15 0.1 0.05 F(x)=P(X<=x) 0.5 0.7 0.85 0.95 1

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