Answer:
6
Step-by-step explanation:
A fair coin is flipped three times. Let X be the number of heads observed. (a) Give both the possible values and probability mass function of X. (b) Find P(X ≥ 1) and P(X > 1). (c) Compute E[X] and V ar(X).
Answer:
a)
The possible values are 0, 1, 2 and 3.
The probability mass function of X is:
P(X = 0) = 0.125
P(X = 1) = 0.375
P(X = 2) = 0.375
P(X = 3) = 0.125
b)
[tex]P(X \geq 1) = 0.875[/tex], [tex]P(X > 1) = 0.5[/tex]
c) E(X) = 1.5, Var(X) = 0.75
Step-by-step explanation:
For it time the coin is flipped, there are only two possible outcomes. Either it comes up heads, or it comes up tails. Each toss is independent of other tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
A fair coin is flipped three times.
This means that [tex]n = 3[/tex]
Fair coin means that it is equally as likely to be heads or tails, so [tex]p = \frac{1}{2} = 0.5[/tex]
a) Give both the possible values and probability mass function of X.
The possible values are from 0 to n, so 0, 1, 2 and 3.
The probability mass function is the probability of each outcome. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125[/tex]
[tex]P(X = 1) = C_{3,1}.(0.5)^{1}.(0.5)^{2} = 0.375[/tex]
[tex]P(X = 2) = C_{3,2}.(0.5)^{2}.(0.5)^{1} = 0.375[/tex]
[tex]P(X = 3) = C_{3,0}.(0.5)^{3}.(0.5)^{0} = 0.125[/tex]
(b) Find P(X ≥ 1) and P(X > 1).
[tex]P(X \geq 1) = P(X = 1) + P(X = 2) + P(X = 3) = 0.375 + 0.375 + 0.125 = 0.875[/tex]
[tex]P(X > 1) = P(X = 2) + P(X = 3) = 0.375 + 0.125 = 0.5[/tex]
(c) Compute E[X] and Var(X).
[tex]E(X) = np = 3*0.5 = 1.5[/tex]
[tex]Var(X) = np(1-p) = 3*0.5*0.5 = 0.75[/tex]
A pair of shoes that originally sold at $30 is now being offered at a 25% discount.
What is its present price?
Answer:
$22.5
Step-by-step explanation:
You will pay $22.5 for a item with original price of $30 when discounted 25%.
Answer:
Refer to explanation
Step-by-step explanation:
The screenshot you put is the correct answer, here's another method to get the same answer:
Find what 25% is.
100% = 30
1% = 30 ÷ 100 = 0.30
25% = 0.30 x 25 = 7.50
Find the price after the 25% discount.
100 - 25 = 75
75% = 30 - 7.50 = 22.50 or 0.30 x 75 = 22.50 (Both solutions give the same answer)
Find the value of k please
What is the first step in solving the equation 9m - 2 = 16?
Add 2 to each side.
Subtract 2 from each side.
Divide each side by 9.
Multiply each side by 9.
Answer: Add 2 to each side
Step-by-step explanation:
9m-2=16
+2 +2
9m=18
Last month, sales were £180 000.
This month, sales reached £196 200.
What percentage increase is this?
%?
-20 greater than or equal to 5w
Hurry!!!
Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive?
A. 29 - n = 41
B. 29 - n = 40
C. 29 + n = 41
D. 29 + n = 40
Answer:
C
Step-by-step explanation:
Trevon started with $29.
After cleaning, his total rose to $41.
Since he received money, we add that amount (n) to his initial amount of money ($29), to equal his total amount ($41)
Someone please help and explain will mark brainliest
Answer:
Lee earns 2x.
They both earn 3x.
Step-by-step explanation:
If mic earns x, and lee earns 2 times as much, it will be x * 2, or 2x. Then adding mic's salary, x, the number will result in 2x+x. This simplifies into 3x.
Which of the following is an example of a reserved power?
A. raising and maintaining a navy
B. declaring war and governing combat
C. establishing and funding a system of public education
D.coining money and fixing the standards of weights and measures
Answer:
B
Step-by-step explanation:
The time of a pendulum varies as the square root of its length. If the length if a pendulum which beats 15seconds is 9cm, find the length that beats 80seconds and the time of a pendulum with length 36cm
Answer:
length= 3.7 ft.
Step-by-step explanation:
T= (square root of length) * k
1.8 seconds = (square root of 3) * k
k= 1.8 seconds / (square root of 3)
a.) T= (square root of 11) k
substituting k:
T=(square root of 11) * 1.8 seconds / (square of 3)
T= 3.4 seconds
b.) 2 seconds = (square root of length) k
substituting k:
2 seconds =(square root of length) 1.8 seconds / (square root of 3)
Divide the equation by 1.8 seconds / (square root of 3):
2 seconds / [1.8 seconds / (square root of 3)] = (square root of length)
10(square root of 3) / 9 = (square root of length)
square both sides:
100/7 ft= length
length= 3.7 ft.
Hope this helps.
Explain answer !
( Will give brainlst)
Geometry Will give Brainlist
Given :
segment AE and segment BD bisect each otherWhich means :
∠BCA and ∠DCE are equal because they are vertically opposite angles. Segment AC = segment CE because the bisector BD divides the segment AE into two equal parts which are segment AC and segment CE.segment BC and segment CD will be equal because bisector AE divides the segment BD into two equal parts which are segment BC and segment CD.Since two sides and one included angle is equal △ACB≅△ECD under the SAS congruence criterion .
This is classwork and i don't understand it at all PLEASE HELP
Answer:
The independent variable is the number of cars
the band washes and the dependent is the number of money they earn
Step-by-step explanation:
Needing some help please
Answer: Should be (4,0)
Step-by-step explanation:
.Given the assignment categories and weights listed below, what overall grade should the student get in the class? Round your answer to one decimal place. please show me how you got this and what steps u did please hurry
Weight. Average
Homework30%. 95
Projects 15%. 80
Tests 50% 77
Attendance 5% 50
Answer: The answer of your over all grade is 81
Step-by-step explanation:
You do the % then you add them together.
like in this picture
HELP ME FAST PLSSS<3
A bottle of juice states that a serving is 1/2 cup. How many servings are in a 2-pint container? (one pint= 2 cups)
Answer: 8 servings
Step-by-step explanation:
1/2 cup + 1/2 cup = 1 cup
> 1 cup + 1 cup = 2 cups = one pint
1/2 cup + 1/2 cup = 1 cup
if 4 servings go in one pint then 8 servings goes in 2 pint
Answer:
8 cups/servings.
Explanation:
Can't explain further more because I'm not good in explaining things yet I'm sure that's the correct answer.
Sofia is a helper for the kindergarten class and is in charge of picking a video for their end-of-year party. To choose which type of movie they would like best, she decided to survey every other child entering a matinee for a cartoon called, “Three Pretty Princesses.” The total number of children surveyed was 40. What is wrong with the way she selected her sample? Check all that apply. ill give brainliest to whoever answers
Answer:
She decided to survey each other child instead of every child
Step-by-step explanation:
Sorry if im wrong
Answer:
so if you have a multie chose it would be A D E
Step-by-step explanation:
Identify the rate of change of the function.
67Answer:67
Step-by-step explanation:
Answer these please. :0
Answer:
I wrote the answers below
Step-by-step explanation:
x+3<70------>0,60
-5x<2--------->3,5
5x<2---------->-3,-1
-3x>18-------->-10,-20
what is the square root of 64
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
8x8=64 so √64=8. hope this helps!
Clark typed 720 words in 18 minutes. How many words can he type in one minute?
Answer:
Clark can type 40 words in one minute
Step-by-step explanation:
Set up a proportion: [tex]\frac{720}{18} = \frac{x}{1}[/tex] Cross multiply, then divide: 720 × 1 = 720, 720 ÷ 18 = 40So, x = 40I hope this helps!
n/10 + 8 = 12. Mental Math Solve the equation
Answer:
= 4 0
Step-by-step explanation:
/ 1 0 + 8 =1 2
/1 0+ 8 − 8 = 1 2 − 8
SIMPLIFY
1 0 = 4
Multiply all terms by the same value to eliminate fraction denominators
1 0 = 4
1 0 ⋅ /1 0= 1 0 ⋅ 4
Simplify
n=40
what single decimal multiplier would you use to decrease by 7% followed by a 20% decrease
Answer:
x 0.27
Step-by-step explanation:
if they are both decreasing then just add the two percentages together then divide by 100 to give you your decimal answer
There are 23 students in ms day”s class. Only 17 students are present today use the model to find A the number of students that are absent
Answer:
6 students are absent.
Doreen Schmidt is a chemist
Answer:
that isnt a question but good to know! :)
Step-by-step explanation:
Liam opened a savings account with a $400 deposit and a simple interest rate of 7.5%. If the balance of the account is now $670 and there are no deposits or withdraws, how long ago did he open the account?
Answer:
If he deposited weekly, he would be depositing 9 dollars each week.
Step-by-step explanation:
Just thank me later and click the crown at the top of this answer if it helped ;)
simplify the expression :
1.7h - 8.9 + 3
Answer:
1.7h - 5.9
Step-by-step explanation:
Combine the like terms -8.9 and 3 to get -5.9. Since it's negative, you subtract.
7 4 9 as an improper fraction
how to Evaluate the expression, given functions f and g: f(x) = 3x - 2, g(x) = 7 – x^2. 3f(1) – 2g(-2)
Suppose f(x)=x+2. Find the graph of f(1/3x)
Answer:
f(x)=x+2.
f(1/3x)=1/3 x+2=(x+6)/3or x/3+2
Answer:
graph 3
Step-by-step explanation: