You have a coin with unknown probability p of coming up heads. You wish to generate a random variable which takes the values 0 and 1, each with probability 1/2. Assume 0 < p < 1. You adopt the following procedure. You start by flipping the coin twice. If both flips produce the same side of the coin, you start again. If the result of the first flip is different from the result of the second flip, you report the result of the first flip, and you are finished (this is a trick originally due to John von Neumann). (a) Show that, in this case, the probability of reporting heads is 1/2. (b) What is the expected number of flips you must make before you report a result?
Answer:
(a) Hence, the probability of reporting heads is 1/2.
(b) Therefore, the expected number of such trial is 1 / 2p (1 –p).
Step-by-step explanation:
Solution:
To generate a random variable takes value 0 and 1.
Let 0 < p <1,
A coin is flipped twice.
(a) Probability of reporting head is 1/2.
The result of two toss is either HT or TH.
In this case we used conditional property, Given that you got either HT or TH,
Probability of occurring head or tail:
P (1ST = H| HT or TH]
= P (H) / P (HT or TH)
= P (HT) / P (HT or TH)
= P (1-P) / P (1-P) + (1-P)P
= P (1-P) / 2P (1-P)
=1/2
Hence, the probability of reporting heads is 1/2.
(b) Expected number of flip before report a result.
The probability of reporting a result on each trial is:
P (HT or TH)
=P (HT) + P (TH)
=P (1-P) + (1 –P) P
= 2P (1 –P)
Since, E(X) = 1 / P
Therefore, the expected number of such trial is 1 / 2p (1 –p).
What is the estimated sum of 503, 472, 486, 499, 539, and 522?
Answer:
3021
Step-by-step explanation:
Answer:
Your answer is: Estimated is: 3,000
The real answer was:
↓
3,021.
Step-by-step explanation:
Hope this helped : )
I have no idea how to do this
Answer:
it's ok!! thats why you have us!! we're here to help!
13/z
have a nice day!! also hope this helps!
Step-by-step explanation:
Answer:
13 on top
Z on the bottom
Step-by-step explanation:
6 plus 7 is 13
Here is a set of signed numbers: 7, -3, 1/2, -0.8, 0.8, -1/10, -2
Order the numbers from least to greatest.
first gets brainllest
Answer:
7, 0.8, 1/2, -0.8, -1/10, -2, -3,
Step-by-step explanation:
accidently put greatest to least just flip it i still want brainliest tho
How do you do these questions and explanations please?
Step-by-step explanation:
1. Standard error is SE = σ / √n. As n increases, SE decreases.
2. Degrees of freedom is d = n − 1. As n increases, d increases.
3. The t statistic is t = (x − μ) / SE. As SE decreases, t increases.
4. As n increases, t* decreases and approaches z*.
5. As the t statistic increases, the P-value decreases.
6. Margin of error is t* times SE. As n increases, MoE decreases.
7. The width of the confidence interval is 2 MoE. As MoE decreases, the width of the confidence interval decreases.
Can you guys help me with this geometry problem tysm
Answer:
m∠UVW = 12°
m∠XYZ = 78°
Step-by-step explanation:
m∠UVW = (x - 10)°
m∠XYZ = (4x - 10)°
∠UVW + ∠XYZ = 90°
(x - 10) + (4x - 10) = 90
x - 10 + 4x - 10 = 90
5x - 20 = 90
5x = 110
x = 22
m∠UVW = (22 - 10)° = 12°
m∠XYZ = (4(22) - 10)° = 78°
Started at 20° and dropped 4° each minute
Answer:
hey mate I couldn't understand ur question.......plz recheck....
Answer:
What's the rest of the question?
Step-by-step explanation:
The table below shows the results of a survey of 1000 American college students and their age breakdown. Use the table to answer questions
Answer:
c
Step-by-step explanation:
Plz answer I will mark u brainiest!!!!
Answer:
65
Step-by-step explanation:
Convert 6 feet to meters.
Conversion table:
1 meter = 3.281 feet
Answer:
6 feet = 1.8288 meters
Step-by-step explanation:
Hope this helps and have a phenominal day!
UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13). The Director of Institutional Research at UCF is interested in testing this information. She decides to conduct a survey of 50 randomly selected recent graduate economic students. The sample mean is $43,350 and the sample standard deviation is 15,000. Alpha = 0.01
Answer:
There is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.
Step-by-step explanation:
In this case we need to test whether the mean starting salary of a graduate with a bachelor in economics is $48,500.
The information provided are:
[tex]\bar x=\$43350\\s=\$15000\\n=50\\\alpha =0.01[/tex]
The hypothesis for the test can be defined as follows:
H₀: The mean starting salary of a graduate with a bachelor in economics is $48,500, i.e. μ = 48500.
Hₐ: The mean starting salary of a graduate with a bachelor in economics is different from $48,500, i.e. μ ≠ 48500.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}[/tex]
[tex]=\frac{43350-48500}{15000/\sqrt{50}}\\\\=-2.42773\\\\\approx -2.43[/tex]
Thus, the test statistic value is -2.43.
Compute the p-value of the test as follows:
[tex]p-value=2\times P(t_{49}>-2.43)=0.0188[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.0188.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.0188 > α = 0.01
The null hypothesis will not be rejected at 1% level of significance.
Thus, concluding that there is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.
are 3,000:18,000 and 10,000:32,000 equivalent
Answer:
No
Step-by-step explanation:
they are not equivalent
emilio worked for 19.5 hours he earned 497.25 how much did he earn per hour?
Answer:
25.5 per hour
Step-by-step explanation:
497.25/19.5
Answer:
497.25 devided by 19.5= $25.5 per hour
Step-by-step explanation:
Anyone willing to answer this?
Answer:
1. perpendicular; the opposite?
2. Parallel; the slopes are the same?
Step-by-step explanation:
Just use Math
way
Which of the following in NOT an equation of a line parallel to the line with equation y=1/2x-6 *
y = 2/4x + 6
y = 0.5x - 3
y = 1/2x + 1
y = 2x - 4
9514 1404 393
Answer:
y = 2x - 4
Step-by-step explanation:
You want an equation with an x-coefficient that is not 1/2.
2/4 = 0.5 = 1/2
so, the first three answer choices don't meet problem requirements.
The line with equation ...
y = 2x -4
is not parallel to y = 1/2x -6.
solve the system of equations
y=x-2
x+y=10
Answer:
Step-by-step explanation:
x + x - 2 = 10
2x - 2 = 10
2x = 12
x = 6
y = 6 -2
y = 4
(6,4)
2x^2+2=3x complete the square i need full explaination ASAP
Answer:
x = 3/4 + √7i/4
x = 3/4 - √7i/4
Step-by-step explanation:
2x² + 2 = 3x
Subtract 3x from both sides so it equals 0:
2x² - 3x + 2 = 0
Divide both sides by 2:
x² - 3/2x + 1 = 0
Subtract 1 from both sides:
x² - 3/2x = -1
Take -3/2 and multiply it by 1/2 then square it:
(-3/2 • 1/2)²
9/16
Add this to both sides:
x² - 3/2x + 9/16 = -1 + 9/16
Rewrite the perfect square on the left and add the terms on the right:
(x - 3/4)² = -7/16
Square root both sides to get rid of the square:
x - 3/4 = ± √-7/16
Simplify the radical:
x - 3/4 = ± √7i/4
Add 3/4 to both sides:
x = 3/4 ± √7i/4
Your two solutions are:
x = 3/4 + √7i/4
x = 3/4 - √7i/4
You can also convert to decimal if you need to (but I don’t recommend it):
x = 0.75 + 0.661438i
x = 0.75 - 0.661438i
Hope this helps!
One number is 2 times another. The sum of their reciprocals is 15 Find the numbers.
Answer:
7.5 i think
Step-by-step explanation:
I need help ASAP. Thank you in advance! The choices are true & false.
10x - 6 = 6x + 6
i need the answer but i think its 3
Answer:
= 3
Step-by-step explanation:
Add 6 to both sides of the equation 10 − 6 = 6 + 6
10x-6=6x+6 10x−6=6x+6
Simplify Add the numbers Add the numbers again 10 = 6 + 12
Subtract 6 from both sides of the equation
10 = 6 + 12
10−6=6+12−6
Simplify
Combine like terms
Combine like terms again
4 = 12
Divide both sides of the equation by the same term
4=12
[tex]\frac{4x}{4}[/tex] =[tex]\frac{12}{4}[/tex]
Simplify Cancel terms that are in both the numerator and denominator then Divide the numbers.
x = 3
John had a baseball cards until he gave x cards away. How many cards does he have now?
Answer:
I don’t think the question makes sense
Write a pair of numbers whose greatest common factor is 10 will give brainlist
Answer:
20 and 10
Step-by-step explanation:
Answer:
20 ,10
Step-by-step explanation:
hope it helps
Instructions
All of the points in the picture are on the same line.
YA
(6, 10)
(a, 8)
(4.b)
(2, 2)
What is the slope
Please help
Find the length of the unknown side. Round your answer to the nearest whole number. (4 points)
Image of a right triangle with legs labeled 12 meters and 8 meters. Hypotenuse is unknown.
13 meters
14 meters
200 meters
208 meters
Answer: 14 meters
Step-by-step explanation:
Pythagorean Theorem formula = a^2 + b^2 = c^2
8^2 + 12^2 = c^
64 + 144 = 208
Now find the square root of 208 = 14.422
Answer:
You answer is 24! hope yhis helps
Step-by-step explanation:
I need help please
Range is y so we set -5x = whatever number you pick from the range values listed, so
-5x = -5 making x=1
-5x = 0 making x=0
-5x = 10 making x=-2
-5x = 15 making x=-3
The domain is {1,0,-2,-3}
Whats the answers please
Answer: D,C,B
Step-by-step explanation:These are the answers
plz help hurry ill give brainllest
Use the number line to determine where to plot each rational number.
4.2 is
StartFraction 7 over 8 EndFraction is
Negative StartFraction 9 over 5 EndFraction is
Answer:
Step-by-step explanation:
Use the number line to determine where to plot each rational number.
4.2 is
✔ between 4 and 5, closer to 4
StartFraction 7 over 8 EndFraction is
✔ between 0 and 1, closer to 1
Negative StartFraction 9 over 5 EndFraction is
✔ between -1 and -2, closer to -2
The number 4.2 is between the 4 and 5, also closer to 4, Agian the number 7/8 between 0 and 1, closer to 1, and -9/5 number between -1 and -2, closer to -2
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have numbers 4.2
The number 4.2 is between the 4 and 5, closer to 4
=7/8 = 0.875
Now 0.875 number between 0 and 1, closer to 1
-9/5 = 1.8
The 1.8 number between -1 and -2, closer to -2
Thus, We can conclude that number 4.2 is between the 4 and 5, closer to 4.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
2.6586 divided by 0.633
Answer:
4.2
Step-by-step explanation:
pls help will give brainliest
Answer:
14 units
Step-by-step explanation:
Answer:
[tex]\sqrt{116[/tex] ( award branliest :) )
Step-by-step explanation:
When you insert both points into the distance formula which is
d = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex] you arrive at the final answer of [tex]\sqrt{116}[/tex]
Chan Hee bought 6.4 pounds of coffee that cost $9.65 per pound. How much did he spend on coffee
?
Answer: $61.76
Step-by-step explanation:
Multiply the price of coffee ($9.65) times the weight (6.4)
=$61.76
Answer:
50.18
Step-by-step explanation:
.