Exercise 3.62. A little boy plays outside in the yard. On his own he would come back inside at a random time uniformly distributed on the interval [0, 1]. (Let us take the units to be hours.) However, if the boy is not back inside in 45 minutes his mother brings him in. Let X be the time when the boy comes back inside (a) Find the cumulative distribution function F of X (b) Find the mean E(X) (c) Find the variance Var(X) Hint. You should see something analogous in Examples 3.20 and 3.38.
a) The cumulative distribution function F of X is: F(x) = P(X ≤ x) = 1
b) The mean E(X) is: E(X) = 0.5 hours.
c) The variance Var(X) is: the variance of X is approximately 0.0833 hours².
To find the cumulative distribution function (CDF) of X, we need to consider two cases: when the boy comes back inside before 45 minutes and when the boy is brought inside by his mother after 45 minutes.
(a) Cumulative Distribution Function (CDF) F of X:
For 0 ≤ x < 0.75 (when the boy comes back inside before 45 minutes):
Since the boy comes back inside uniformly distributed on the interval [0, 1], the CDF is simply the probability that the boy comes back inside before time x.
The probability of the boy coming back inside before x is equal to x, as it is a uniform distribution.
F(x) = P(X ≤ x) = x
For 0.75 ≤ x ≤ 1 (when the mother brings the boy inside after 45 minutes):
If the boy is not back inside at 45 minutes (0.75 hours), his mother brings him inside.
Therefore, the probability of the boy coming back inside before x in this case is 1.
F(x) = P(X ≤ x) = 1
(b) Mean (Expected Value) E(X):
The expected value of X, denoted by E(X), is the average time the boy spends outside before coming back inside.
For a uniform distribution on the interval [0, 1], the expected value is the midpoint of the interval.
Therefore, E(X) = (1 + 0) / 2 = 0.5 hours.
(c) Variance Var(X):
The variance of X, denoted by Var(X), measures the spread or variability of the random variable X around its mean.
For a uniform distribution on the interval [0, 1], the variance is given by:
Var(X) = (1² - 0²) / 12 = 1 / 12 ≈ 0.0833 hours²
So, the variance of X is approximately 0.0833 hours².
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Answer:
they all go straight across
Step-by-step explanation:
Answer:
Go across from each
Step-by-step explanation:
Find the value that makes the proportion true.
Answer:
can not see page
Step-by-step explanation:
mike made 5 fewer than three times the number of bracelets that sheri made. Write an expression to represent the number of brackets mike made. then determine the number of bracelets that mike made if sheri made 12 bracelets
Answer:
the answers are in the pic
Step-by-step explanation:
A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 115,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 6% each year. How many total fish did the company catch over the first 20 years, to the nearest whole number?
Answer:
Rounded to the nearest whole number, the company caught 1,360,630 fish in total over the 20 years.
Step-by-step explanation:
Given that a major fishing company does its fishing in a local lake, and the first year of the company's operations it managed to catch 115,000 fish but due to population decreases, the number of fish the company was able to catch decreased by 6% each year, to determine how many total fish did the company catch over the first 20 years, to the nearest whole number, the following calculation must be performed:
Year 1: 115,000
Year 2: 115,000 x 0.94 = 108,100
Year 3: 108,100 x 0.94 = 101,614
Year 4: 101,614 x 0.94 = 95,517.16
Year 5: 95,517.16 x 0.94 = 89,786.13
Year 6: 89,786.13 x 0.94 = 84,398.96
Year 7: 84,398.96 x 0.94 = 79,335.02
Year 8: 79,335.02 x 0.94 = 74,574.92
Year 9: 74,574.92 x 0.94 = 70,100.42
Year 10: 70,100.42 x 0.94 = 65,894.40
Year 11: 65,894.40 x 0.94 = 61,940.73
Year 12: 61,940.73 x 0.94 = 58,824.29
Year 13: 58,824.29 x 0.94 = 54,730.83
Year 14: 54,730.83 x 0.94 = 51,446.98
Year 15: 51,446.98 x 0.94 = 48,360.16
Year 16: 48,360.16 x 0.94 = 45,458.55
Year 17: 45,458.55 x 0.94 = 42,731.03
Year 18: 42,731.03 x 0.94 = 40,167.17
Year 19: 40,167.17 x 0.94 = 37,757.14
Year 20: 37,757.14 x 0.94 = 35,491.71
TOTAL: 1,360,629.60
Thus, rounded to the nearest whole number, the company caught 1,360,630 fish in total over the 20 years.
Which of the figures appear to to congruent
Answer:
C.
Step-by-step explanation:
What value would make the equation 8x = -72 true?
Answer:x= -9
Step-by-step explanation: You would dive both sides by 8 and -72 divided by 8 is -9
Answer:-9
Step-by-step explanation:
The answer is -9 because we are solving to get x by itself. Since 8 is being multiplied by x the opposite of multiplication is division. Divide both sides by 8 to get x by itself. -72 divided by 8 is -9 because a negative divided or multiplied by a positive is a negative. To check your work you can do 8 times -9 which equals -72.
plz help out zhavia out she keeps on texting me while im trying to work
Answer:
Step-by-step explanation:
increase ≤ 55-43.5
increase ≤ 11.5
Elanor can increase her speed by 11.5 miles per hour.
Expand t (4t - 4 ) answer if you can plz
Answer:
42−4
Step-by-step explanation:
Answer:
4t^2 −4t
Step-by-step explanation:
t(4t−4)
Use the distributive property to multiply t by 4t−4.
4t^2 −4t
What is the slope of the line X=-3?
Answer:
undefined
Step-by-step explanation:
Answer:
The slope is undefined
Step-by-step explanation:
A ship caption is mapping
Please help me lol ......................
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
simple logic
Ahmad made a shirt using 1/4 yards of yellow fabric and 1/8 yards of red fabric. How many more yards of yellow fabric did Ahmad use?
Answer: 1/8
Step-by-step explanation:
convert 1/4 to eighths
1/4 x 2 = 2/8
2/8 yellow fabric - 1/8 red fabric = 1/8
A polynomial is graphed. What could the equation of p?
P(c)=(x+3)(c+1)(2x+1)
Answer:
The answer is B.) p(x)=x(x−2)(2x−7)
Step-by-step explanation:
Khan academy
Simplify the expression 10 + 2(n + 5) + 4n
Answer:
6n + 20
Step-by-step explanation:
10 + 2n + 10 +4n
6n +20
Answer:
[tex]10 + 2n + 10 + 4n \\ 6n + 20 \\ 2(3n + 10)[/tex]
the difference of p and 7 is 30
Answer:
p = 37
p- 7=30
add seven to both sides and you get
p=37
0 + 12 and 0 *
O Yes; Identity Property
O Yes; Associative Property
O Yes; Commutative Property
O Yes; Inverse Property
O Expressions are not equal
Answer:
Yes; Identity Property..
I hope it helps...
#4 Find the value of x and y 34° 109° x and y
A developer has 24.5 acres of land. She buys an adjacent plot of land and increases the total
acreage she owns by 20%. Circle the numbers that make the statements true.
Answer:
The developer bought 4.9 acres of land, increasing its property to 29.4 acres.
Step-by-step explanation:
Given that a developer has 24.5 acres of land, and she buys an adjacent plot of land and increases the total acreage she owns by 20%, to determine the amount of acres she bought and the total acres she now owns, the following calculations must be done:
24.5 x 1.2 = 29.4
24.5 x 0.2 = 4.9
Thus, the developer bought 4.9 acres of land, increasing its property to 29.4 acres.
ANSWER CORRECTLY WITH REASONING FOR BRAINLIEST
Jaya wants to find out what type of art her fellow students enjoy the most. She asks her classmates: "What is your favorite type of art?"
This question is biased.
True
False
Answer:false
Step-by-step explanation:because jaya is not giving her opinion she is asking for others opinions.
What is the final cost of an item priced at $5.70 after a 7% sale tax is applied
Answer:
the total is $6.10 once applied
and the sale tax is $0.40
Step-by-step explanation:
In 1960 sociologists studied a random sample of 1,018 families that consisted of a husband, a wife, and at least one child. Of those families, 5.8 percent reported that the wife was the primary wage earner of the family. In 2011 the study was replicated with a random sample of 1,013 families that consisted of a husband, a wife, and at least one child. Of those families, 22.3 percent reported that the wife was the primary wage earner of the family. Which of the following represents a 99 percent confidence interval for the difference between the proportions of families that consisted of a husband, a wife, and at least one child from 1960 to 2011 that would have reported the wife as the primary wage carner? (0.223)(0.777) (0.058) (0.942)
(A) (0.223-0.058) 1.96L03 ) (223-0058) ±196 1.013 1 1.018
(B) (0.223-0058) 226(07,(0580942 1,013 1,018
(C) (0.223-0058)2.576, (02230772)(0.45810942 (0.058)(0.942) 1,018
(D) (0.223-0.058) t2.326, 2,031 1,013 1.018
(E) (0.223-0058)?2.57612031(1.013 +1.18
Answer:
(0.223 - 0.058) ± 2.576 * sqrt[((0.223)(0.777))/1018 - ((0.058)(0.942))/1013]
Step-by-step explanation:
Given that :
P1 = 22.3% = 0.223
q1 = 1 - P1 = 1 - 0.223 = 0.777
Sample size, n1 = 1018
P2 = 5.8% = 0.058
q2 = 1 - P2 = 1 - 0.058 = 0.942
Sample size, n2 = 1013
Confidence level, Zcritical at 99% = 2.576
Using the relation :
(P1 - P2) ± Zcritical * Sqrt[(P1q1/n1 + P2q2/n2)
(0.223 - 0.058) ± 2.58 * sqrt[((0.223)(0.777))/1018 - ((0.058)(0.942))/1013]
The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.
10x3 + 35x2 − 4x − 14
5x2(____) − 2(____)
What is the common factor that is missing from both sets of parentheses?
−2x − 7
2x + 7
−2x2 + 7
2x2 + 7
5x2( 2x + 7 ) − 2( 2x + 7 ) that's it.
Answer:
b
Step-by-step explanation:
FASTTTTTTTTTTTTTTTTTTTTTT 50 POINTS +BRAINLIEST
Answer:
[tex]\huge\boxed{\sf Option \ 2}[/tex]
Step-by-step explanation:
[tex]\sf (\frac{4}{5})^3 \\\\[/tex]
This means that 4/5 repeats itself 3 times.
So,
[tex]\sf = \frac{4}{5} * \frac{4}{5} * \frac{4}{5} \\\\= \frac{64}{125} \\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer: Choice 2: 4/5 • 4/5 • 4/5 = 64/125
Step-by-step explanation: The exponent tells you how many times you have to multiply the 4/5. Since the exponent is 3, we know to multiply 4/5 with itself 3 times, like this: 4/5 • 4/5 • 4/5, which will get us 64/125
Graph the following features:
Slope =-3/5
Y-intercept = 3
Answer:
ummm how about noooooooooooooooooo
The Blinking Rockets baseball team has had 127,034 visitors to their fan website. Rounded to the nearest ten thousand how many visitors have they had
Answer:
[tex]Visitors = 130000[/tex]
Step-by-step explanation:
Given
[tex]Visitors = 127034[/tex]
Required
Approximate to the nearest ten thousand
First, identify the digit at the ten thousand position
From the given numbers of visitors, the digit is 2.
So, the next digit (which is 7) will be approximated and added to 2.
7 > 5. So, 1 will be added to 2.
The number of visitors becomes:
[tex]Visitors = 130000[/tex]
The equation y = -3 is a example of linear function. Why?
Explanation:
We can rewrite y = -3 as y = 0x-3 or y = 0x+(-3)
Compare that to y = mx+b and we can see that m = 0 is the slope and b = -3 is the y intercept. The slope of 0 indicates a horizontal line.
We can think of it is as slope = rise/run = 0/1 = 0. A rise of 0 tells the reader "the graph does not go up or down at all". Every point on the line y = -3 has y coordinate of -3. Two such points are (0,-3) and (1,-3).
At a school, 153 students play at least one sport. This is 75% of the students at the school. How many students are at the school?
Answer:
204 people
Step-by-step explanation:
i used a calculator
which expression would be easier to simplify if you used the commutative property to change the order of the numbers
Answer:
D
Step-by-step explanation:
Answer:
Hi There :)
If your talking about the question:
which expression would be easier to simplify if you used the commutative property to change the order of the numbers
A. -10 (-20) + 1/2
B. 60 + 40 + (-25)
C. 30 + (-12) + 70
D. 1/3 + 2/3 + (- 1/4)
Then the answer would be
C. 30 + (-12) + 70
Hope this helps :)
A theater owner wants to provide enough seating for 928 people. The main floor has 25 rows of 22 seats in each row. If the balcony has 21 rows, how many seats must be in each row to satisfy the owner’s seating requirements?
Answer:
18 seats in each row
Step-by-step explanation:
25 x 22 = 550
928 - 550 = 378
378 / 21 = 18