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Chapter 4: Q. 4.19 (page 164)

If the distribution function of Xis given by

F(b)=0鈥呪赌呪赌呪赌�b<012鈥呪赌呪赌呪赌�0鈮�b<135鈥呪赌呪赌呪赌�1鈮�b<245鈥呪赌呪赌呪赌�2鈮�b<3910鈥呪赌呪赌呪赌�3鈮�b<3.51鈥呪赌呪赌呪赌�b鈮�3.5

calculate the probability mass function of X.

Short Answer

Expert verified

p(x)=12鈥呪赌呪赌呪赌�x=0110鈥呪赌呪赌呪赌�x=115鈥呪赌呪赌呪赌�x=2110鈥呪赌呪赌呪赌�x=3110鈥呪赌呪赌呪赌�x=3.5

Step by step solution

01

Given information

F(b)=0鈥呪赌呪赌呪赌�b<012鈥呪赌呪赌呪赌�0鈮�b<135鈥呪赌呪赌呪赌�1鈮�b<245鈥呪赌呪赌呪赌�2鈮�b<3910鈥呪赌呪赌呪赌�3鈮�b<3.51鈥呪赌呪赌呪赌�b鈮�3.5

02

Explanation

The probability mass procedure is equivalent to zero for every particular where the distribution function is locally equivalent to some consistent. Therefore, we only have to think of facts in which function Fhas a brake.

Here,

P(0)=F(0)-P(b<0)

=12

P(1)=35-12

=110

P(2)=45-35

=15

P(3)=910-45

=110

P(3.5)=1-910

=110

03

Final answer

Probability mass function is

p(x)=12鈥呪赌呪赌呪赌�x=0110鈥呪赌呪赌呪赌�x=115鈥呪赌呪赌呪赌�x=2110鈥呪赌呪赌呪赌�x=3110鈥呪赌呪赌呪赌�x=3.5

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Most popular questions from this chapter

When coin 1 is flipped, it lands on heads with probability .4; when coin 2 is flipped, it lands on heads with probability .7. One of these coins is randomly chosen and flipped 10 times.

(a) What is the probability that the coin lands on heads on exactly 7 of the 10 flips?

(b) Given that the first of these 10 flips lands heads, what is the conditional probability that exactly 7 of the 10 flips land on heads?

Let Xbe a Poisson random variable with parameter 位. What value of 位maximizes P{X=k},k鈮�0?

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?

Compare the Poisson approximation with the correct binomial probability for the following cases:

(a)P{X=2}whenn=8,p=.1;

(b)P{X=9}whenn=10,p=.95;

(c)P{X=0}whenn=10,p=.1;

(d) P{X=4}whenn=9,p=.2.

A ball is drawn from an urn containing 3white and 3black balls. After the ball is drawn, it is replaced and another ball is drawn. This process goes on indefinitely. What is the probability that the first 4balls drawn, exactly2 are white?
See all solutions

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