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Chapter 4: Q. 4.19 (page 164)

If the distribution function of Xis given by

F(b)=0    b<012    0≤b<135    1≤b<245    2≤b<3910    3≤b<3.51    b≥3.5

calculate the probability mass function of X.

Short Answer

Expert verified

p(x)=12    x=0110    x=115    x=2110    x=3110    x=3.5

Step by step solution

01

Given information

F(b)=0    b<012    0≤b<135    1≤b<245    2≤b<3910    3≤b<3.51    b≥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    x=0110    x=115    x=2110    x=3110    x=3.5

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Most popular questions from this chapter

A student is getting ready to take an important oral examination and is concerned about the possibility of having an “on” day or an “off” day. He figures that if he has an on the day, then each of his examiners will pass him, independently of one another, with probability8, whereas if he has an off day, this probability will be reduced to4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on the day, should he request an examination with3examiners or with5examiners?

Let N be a nonnegative integer-valued random variable. For nonnegative values aj, j Ú 1, show that

∑j=1∞a1+…+ajP{N=j}=∑i=1∞aiP[N≥i}

Then show that

E[N]=∑i=1∞P[N≥i}

and

E[N(N+1)]=2∑i=1∞iP{N≥i}

In Example 4b, suppose that the department store incurs an additional cost of cfor each unit of unmet demand. (This type of cost is often referred to as a goodwill cost because the store loses the goodwill of those customers whose demands it cannot meet.) Compute the expected profit when the store stocks s units, and determine the value of data-custom-editor="chemistry" s that maximizes the expected profit.

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?

Repeat Example 1Cwhen the balls are selected with replacement.
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