We are given i.i.d. Bernoulli trials with success probability p, and we need to find the conditional probability mass function of Sm, given Sn-k. The distribution that arises in this problem is the binomial distribution.
The binomial distribution is the probability distribution of the number of successes in a sequence of n independent Bernoulli trials, with a constant success probability p. In this problem, we are considering a subsequence of n-k trials, and we need to find the conditional probability mass function of the number of successes in a subsequence of m trials, given the number of successes in the remaining n-k trials. Since the Bernoulli trials are independent and identically distributed, the probability of having k successes in the remaining n-k trials is given by the binomial distribution with parameters n-k and p.
Using the definition of conditional probability, we can write:
P(Sm = s | Sn-k = k) = P(Sm = s and Sn-k = k) / P(Sn-k = k)
=[tex]P(Sm = s)P(Sn-k = k-s) / P(Sn-k = k)[/tex]
=[tex](n-k choose s)(p^s)(1-p)^(m-s) / (n choose k)(p^k)(1-p)^(n-k)[/tex]
where (n choose k) =n! / (k!(n-k)!) is the binomial coefficient.
We can use this conditional probability mass function to find E[Sm | Sn-k]. By the law of total expectation, we have:
[tex]E[Sm] = E[E[Sm | Sn-k]][/tex]
=c[tex]sum{k=0 to n} E[Sm | Sn-k] P(Sn-k = k)\\= sum{k=0 to n} (m(k/n)) P(Sn-k = k)[/tex]
where we have used the fact that E[Sm | Sn-k] = mp in the binomial distribution.
Thus, the conditional probability mass function of Sm, given Sn-k, leads to an expression for the expected value of Sm in terms of the probabilities of Sn-k.
Learn more about bernoulli here:
https://brainly.com/question/30509621
#SPJ11
the sum of two consecutive multiples of 4 is 36 . find the multiples ???
PLZZZZZZZZZ help me now
Answer:
The numbers are 16 and 20
Step-by-step explanation:
Let the multiples be: x+4 and x+8
Sum is 36, so we can make an equation:
x+4+x+8=36
2x=36-12
x=12
The numbers are 12+4=16, 12+8=20.
Hope this answer helped you! If so, please leave a rating and let me know if I was correct. (Hopefully Brainliest, but totally up to you.) Have a great day!
Find the measure......
Answer:
the answer would be S/ 2= 140/ 2 = 70°
HELP ASAP! EXPONENTIAL FUNCTIONS
Dont be shy- drop the answer :)
Answer:
-11x = -55
x = 5
Step-by-step explanation:
Hope that helps!
Jack made 9 identical bags using 5 yards of fabric. How much fabric did Jack use for each bag? Solve on paper and check your work on Zearn.
Answer: 5/9 yards
Step-by-step explanation:
From the question, we are informed that Jack made 9 identical bags using 5 yards of fabric.
To calculate the amount of fabric that Jack use for each bag, we have to divide 5 by 9. Thus will be:
= 5 / 9
Therefore, it means that Jack used 5/9 yards for each bag
If I have $25.2, would it be $25.02 or $25.20?
Answer:
You would have $25.20
if it was 25.02 the 0 would be included, money can be rounded like this too
Answer:
Yeah he/she is correct because I did that too.
Step-by-step explanation:
Express the function F in the form f ∘ g. (Enter your answers as a comma-separated list. Use non-identity functions for f(x) and g(x).) F(x) = x + 2
Answer:
[tex]F(x) = f \circ g[/tex]
[tex]f(x) = x + 2[/tex] and [tex]g(x) = x[/tex]
Step-by-step explanation:
Given
[tex]F(x) = x + 2[/tex]
Required
Express as
[tex]F(x) = f \circ g(x)[/tex]
In functions:
[tex]f \circ\ g(x) = f(g(x))[/tex]
So, we have:
[tex]f(g(x)) = x + 2[/tex]
g(x) can be set to x and f(x) to x + 2
Hence:
[tex]F(x) = f \circ g[/tex]
When: [tex]f(x) = x + 2[/tex] and [tex]g(x) = x[/tex]
18,000 divided by 25%
Answer:
4500
Step-by-step explanation:
18000 / 100 =180
180*25 = 4500
graph the linear equation y = -6x - 5
this was my answer from demos
Si 2X -7 = 3, luego 3X + 1 =
(1) 4
(2)5
(3)7
(4)12
(5)16
Answer:
2x-7=3
2x=3+7
{2x=10}÷2
x=5
꧁꧁꧂꧂
3x+1=
{3x=1}÷3
x=1/3
how muck is in kilograms?
Answer:
1000grams= 1 kilogram
Step-by-step explanation:
Answer:
1000 grams = 1 Kilo
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 8463160
Step-by-step explanation:
Answer:
8463160
Step-by-step explanation:
https://byjus.com/rounding-to-the-nearest-tenth-calculator/
.
Simplify the radical expression.
−4x2
2x2
−2x2
4x2
Find the volume of the cylinder.
Either enter an exact answer in terms of it or use 3.14 for
CAN SOMEONE HELP LIKE RN I NEED IT QUICK
A newspaper invited readers to call a telephone number and record their comments. The next day they reported that readers overwhelmingly prefer two-way traffic flow to one-way streets. This is an example of: A. A convenience sample B. A self-selected sample C. A systematic sample D. A random sample does anyone know the answer
Answer: Self selected sample
Step-by-step explanation:
They people chose themselves
This is an example of: B. A self-selected sample , Option B is the answer.
What is a self-selected sample ?A self selected sampling technique is one in which the researcher puts out a call or publicises so that individuals and organisations can take part in the survey on their own will which saves the time for searching for the appropriate people .
It is given that
A newspaper invited readers to call a telephone number and record their comments.
This is an example of: B. A self-selected sample
Therefore Option B is the answer.
To know more about Self Selected Sample
https://brainly.com/question/27383518
#SPJ2
1. Which of the following equations would NOT contain the point (4,12)?
A. y=-1/2x+14
B. y=1/2x+8
C.y=-2x+20
D.y=3/4x+9
Answer:
the answer is b hope this helps :)
PLEASE HELP!!
The cost to rent a chain saw for two days and a brush chipper for two days is $272. The cost to rent a
chain saw for two days and a brush chipper for one day is $195. Write a system of equation to solve to
find the cost of renting a chain saw for one day.
59:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
B
39
15
36
Find tan A
a
5
tan A =
13
C.
5
tan A -
12
b.
13
d.
12
tan A =
tan A -
5
Answer:
Step-by-step explanation:
find the m and b of the table
9514 1404 393
Answer:
m = 1/2
b = -7
Step-by-step explanation:
The formulas for these can be used.
m = (y2 -y1)/(x2 -x1) . . . . . . . . . formula for slope given 2 points
m = (-9 -(-11))/(-4-(-8)) = 2/4
m = 1/2
__
b = y1 -m·x1 . . . . . . . . . . . . formula for y-intercept given slope and point
b = -11 -(1/2)(-8) = -11 +4
b = -7
I NEED HELP ASAP WILL GIVE BRAINLYEST
Answer:
-8
Step-by-step explanation:
First simplify the expression to -(2^5)^3/5. Then you get -2^3, which is simplified again to -8.
A leisure aircraft is owned by the Broadland Flying Group which has 10 members. The costs of keeping the aircraft comprise maintenance costs (including insurance) and the running cost which is mainly fuel. Average fuel consumption is 9 miles per gallon. If the 10 members of the Group are to share costs equally, write down a formula to enable Gordon the treasurer to calculate the annual cost for each member if the aircraft travels n miles in a year, incurs maintenance costs of £M and fuel costs £3 a gallon.
Answer:
£(M + n/3) / 10
Step-by-step explanation:
Given that :
Number of members = 10
Fuel consumption = 9 miles per gallon
Consumption for n miles = n/9 GALLONS
Cost of fuel = n/ 9 * £3 = 3n / 9 = £n / 3
Maintainace cost = £M
Annual cost per member :
£(M + n/3) / 10
Find the area of the circle 18in
1017.88in^2
You need to use pi
Answer:
1017.88inches^2
Step-by-step explanation:
Area of a circle=pi * radius^2
324*pi=1017.88
Plz help me with 18 is not -0.95
Answer:
Please refer to the attachment.......
You get scores of 72 and 88 on 2 science tests. You have to have an average of at least 85 to not be grounded by your parents. What score do you need to make on your next test to not be grounded?
Answer:
95
Step-by-step explanation:
72+88+95=255:3= 85
Micah invests $5,280 in an account that earns 4.2% interest, compounded monthly.
Part A
Write a function for the amount that will be in the account after t years.
Part B
What is the value of the account after 8 years?
a) The function is given as follows: [tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]
b) The value of the account after 8 years is given as follows: $7,384.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameter values for this problem are given as follows:
P = 5280, r = 0.042, n = 12.
Hence the equation is given as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]
The value of the account after 8 years is obtained as follows:
[tex]A(8) = 5280\left(1 + \frac{0.042}{12}\right)^{12 \times 8}[/tex]
A(8) = $7,384.
More can be learned about compound interest at https://brainly.com/question/24274034
#SPJ1
coat is 20% off. If the regular price of the coat is $225, what is the sale price of the coat?
Answer:
$180
Step-by-step explanation:
$225 times .20 = 45 . 225-45=180
Answer:
$180
Step-by-step explanation:
Find 1% of the price.
100% = 225
1% = 225 ÷ 100 = 2.25
100 - 20 = 80% (Percentage of sale price)
80% = 2.25 x 80 = 180
A 2-year loan of $500 is made with 4% simple interest.Find the interest earned
Answer:
$40
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 500(.04)(2)
Based on the information given the interest earned is $40.
Using this formula
Interest =Principal× Rate× Time
Where:
Time =2 year
Principal=$500
Rate=4% or 0.04
Let plug in the formula
Interest=500(0.04)(2)
Interest=$40
Inconclusion the interest earned is $40.
Learn more here:https://brainly.com/question/20981855
Vincent had 97 rocks in his collection. He found 48 more at the beach. How many did he have in all ?
Answer:
145
Step-by-step explanation:
97+48
7+8=15
9+4+1=14
145
What is the solution to the equation 3^x = 10?
Answer:
log3 (10) = x
the 3 is a tiny 3
Step-by-step explanation:
remember the saying, left right left.
so, 3 goes to the left, x goes to the right, and 10 goes to the left side of the equal sign which in turn comes out to log3(10) =x