/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.5.3 聽Consider the functionf(x)聽=聽... [FREE SOLUTION] | 91影视

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Chapter 5: Q.5.3 (page 212)

Consider the function

f(x)=C(2x鈭�x3)0<x<520otherwise

Could fbe a probability density function? If so, determine

C. Repeat if f(x)were given by

localid="1646632841793" f(x)=C(2x鈭�x3)0<x<520otherwise

Short Answer

Expert verified

Whenc=0,卤2thenf(x)<0

Step by step solution

01

Given Information

f(x)=C(2x鈭�x3)0<x<520otherwise

02

Explanation

2x-x3=-x(x-2)(x+2)

c=0

鈭�-鈭�鈭�f(x)dx=0,鈭�-鈭�鈭�f(x)dx=1

c>0,f(x)<0,x鈭�(2,52)

03

Explanation

c=2

f(x)=2(2x-x3)=4x-2x3

f(x)<0,x鈭�(2,52)

f(1.5)=4脳15-2脳(1.5)3=-0.75

c<0,f(x)<0(0,2)

04

Explanation

c=-2

f(x)=-2(2x-x3)

role="math" localid="1646639321144" =-4x+2x3

f(1)=-4+(2脳1)=-2

f(x)鈮�0

05

Explanation

f(x)=C(2x鈭�x3)0<x<520otherwise

2x-x2=-x(x-2)

c=0,鈭�-鈭�鈭�f(x)dx=0

c>0,f(x)<0,x鈭�(2,52)

06

Explanation

x=2.2

f(2.2)=4(2.2)-2(2.2)=-0.88

c<0,x鈭�(0,2)

c=-2,f(x)=-4x+2x2

f(1)=-4+2=-2<0

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Most popular questions from this chapter

One thousand independent rolls of a fair die will be made. Compute an approximation to the probability that the number 6will appear between 150and 200times inclusively. If the number 6appears exactly 200times, find the probability that the number 5 will appear less than 150times.

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by

f(x)=10x2x>100x鈮�10

(a)FindP{X>20}

localid="1646589462481" (b)What is the cumulative distribution function of localid="1646589521172" X?

localid="1646589534997" (c)) What is the probability that of6such types of devices, at least localid="1646589580632" 3will function for at least localid="1646589593287" 15hours? What assumptions are you making?

A model for the movement of a stock supposes that if the present price of the stock is s, then after one period, it will be either us with probability p or ds with probability 1鈭�p. Assuming that successive movements are independent, approximate the probability that the stock鈥檚 price will be up at least 30 percent after the next 1000 periods ifu=1.012,d=0.990,andp=.52.

The random variable Xhas the probability density function

f(x)=ax+bx20<x<10otherwise

If E[X]=6, find

(a) P{X<12}and

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Show thatE[Y]=鈭�0鈭�PY>ydy-鈭�0鈭�PY<-ydy.

Hint: Show that 鈭�0鈭�PY<-ydy=-鈭�-鈭�0xfy(x)dx

鈭�0鈭�PY>ydy=鈭�0鈭�xfy(x)dx
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