# probability

Sophia is vacationing in Monte Carlo. On any given night, she takes X dollars to the casino and returns with Y dollars. The random variable X has the PDF shown in the figure. Conditional on X=x , the continuous random variable Y is uniformly distributed between zero and 3x .

1. Find the PDF of Z . Express your answers in terms of z using standard notation.

If −40<z<0 :
fZ(z)=

If 0<z<80 :
fZ(z)=

If z<−40 or z>80 :
fZ(z)=

2. What is E[Z] ?

E[Z]=

1. 👍 3
2. 👎 1
3. 👁 2,250
1. 1:
1/2400
0

2:
2/3

3:
(40+z)/2400
0

4:

5/7 result

1. 👍 5
2. 👎 1
2. 3.
c. 0

4. 40/3

1. 👍 5
2. 👎 1
3. 3.
b) (-z/4800)+(1/60)

1. 👍 4
2. 👎 1

## Similar Questions

1. ### Probability

Sophia is vacationing in Monte Carlo. On any given night, she takes X dollars to the casino and returns with Y dollars. The random variable X has the PDF shown in the figure. Conditional on X=x , the continuous random variable Y

2. ### algebra 2

A stadium has 49,000 seats. Seats sell for 25 dollars in Section A, 20 dollars in Section B, and 15 dollars in section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium

3. ### Math

Sophia buys an eqaul number of oranges and pears for a party. The oranges are bought at a price of 7 for \$2 and the pears are bought at a price of 5 for \$3. She pays \$33 more for the pears than the oranges. How much does Sophia

4. ### math

I have 200 canadian dollars and exchange them for 1/5 fewer us dollars. After spending 3/4 of my us dollars how much do I have left?

1. ### probability

Paul is vacationing in Monte Carlo. On any given night, he takes X dollars to the casino and returns with Y dollars. The random variable X has the PDF shown in the figure. Conditional on X=x, the continuous random variable Y is

2. ### social

how long did hagia sophia take to build?

3. ### Algebra

Andrew needs x dollars for a snack. Scott needs 2 more dollars than Andrew, but Nick only needs half as many dollars as Andrew. Altogether they need \$17 to pay for their snacks. How many dollars does Nick need? Thanks so much!

4. ### World History

From AD 527 to 565, Justinian I was the first ruler of the Byzantine Empire (1). During his reign, the empire encompassed most of the land around the Mediterranean Sea (2). Under his rule, magnificent monuments were built

1. ### Language Arts

Harlem Night Song This is the poem Come, Let us roam the night together Singing. I love you. Across The Harlem roof-tops Moon is shining. Night sky is blue. Stars are great drops Of golden dew. Down the street A band is playing. I

2. ### ENGLISH

An angel, robed in spotless white, Bent down and kissed the sleeping Night. Night woke to blush; the sprite was gone. Men saw the blush and called it Dawn. Paul Laurence Dunbar I have a few questions on this poem which I do not

3. ### math

greg exchanged 200 canadian dollars for 1/5 fewer u.s dollars. after spending 3/4 of the u.s dollars, how many did he have left?

4. ### math

labor. Let y be the costAn electrician charges a 45.00 dollars travel fee plus 30.00 dollars per hour of in dollars for x hours of work. Write the slope-intercept form of the equation.