A fair coin is flipped 15 times. Each flip is independent. What is the probability of getting more than ten heads? Let
X = the number of heads in 15 flips of the fair coin.
X takes on the values 0, 1, 2, 3, ..., 15. Since the coin is fair,
p = 0.5 and
q = 0.5. The number of trials is
n = 15. State the probability question mathematically.
P (
X >10)
Try it
A fair, six-sided die is rolled ten times. Each roll is independent. You want to find the probability of rolling a one more than three times. State the probability question mathematically.
P (
X >3)
Approximately 70% of statistics students do their homework in time for it to be collected and graded. Each student does homework independently. In a statistics class of 50 students, what is the probability that at least 40 will do their homework on time? Students are selected randomly.
a. This is a binomial problem because there is only a success or a __________, there are a fixed number of trials, and the probability of a success is 0.70 for each trial.
a. failure
b. If we are interested in the number of students who do their homework on time, then how do we define
X ?
b.
X = the number of statistics students who do their homework on time
c. What values does
x take on?
c. 0, 1, 2, …, 50
d. What is a "failure," in words?
d. Failure is defined as a student who does not complete his or her homework on time.
The probability of a success is
p = 0.70. The number of trials is
n = 50.
e. If
p +
q = 1, then what is
q ?
e.
q = 0.30
f. The words "at least" translate as what kind of inequality for the probability question
P (
X ____ 40).
f. greater than or equal to (≥)
The probability question is
P (
X ≥ 40).
Try it
Sixty-five percent of people pass the state driver’s exam on the first try. A group of 50 individuals who have taken the driver’s exam is randomly selected. Give two reasons why this is a binomial problem.
This is a binomial problem because there is only a success or a failure, and there are a definite number of trials. The probability of a success stays the same for each trial.
Notation for the binomial:
B = binomial probability distribution function
X ~
B (
n ,
p )
Read this as "
X is a random variable with a binomial distribution." The parameters are
n and
p ;
n = number of trials,
p = probability of a success on each trial.
Binomial formula
P (
X =
x )=
$\left(\begin{array}{c}n\\ x\end{array}\right)p^{x}q^{\mathrm{n-x}}$
$p^{x}$ is the probability of
x successes in
x independent and identical trials. For example, if the probability of success = 0.4, the probability of five successes in five independent and identical trials is
$q^{\mathrm{n-x}}$ is the probability of
n - x failures in
n - x identical and independent trials. For example, if the probability of success = 0.4, then the probability of failure is 1 -
p = 0.6. If there are eight trials (
n = 8) with five successes (
x = 5 ), then there were three failures in the eight trials (
n - x = 8 - 5 = 3). The probability of three failures in three independent and identical trials is
$\left(\begin{array}{c}n\\ x\end{array}\right)$ represents the number of combinations of
x successes in
n trials. If there are eight trials (
n = 8) and five successes (
x = 5), then there are 56 possible ways to arrange five successes among eight trials.
The formula
P (
X =
x )=
$\left(\begin{array}{c}n\\ x\end{array}\right)p^{x}q^{\mathrm{n-x}}$ is the probability of
x successes in
n independent and identical trials. If there are eight independent and identical trials, the probability of five successes where
p = 0.4 is
not much
For functions, there are two conditions for a function to be the inverse function:
1--- g(f(x)) = x for all x in the domain of f
2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Source:
OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
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