This module introduces the concept in probability distributions, such as probability mass function(pmf), cumulative distribution function(cdf) and probability density function(pdf).
The distribution
of a random variable
is simply a
probability measure which assigns probabilities to events on thereal line. The distribution
answers questions of the form:
What is the probability that
lies in some subset
of the real
line?
In practice we summarize
by its
Probability Mass Function - pmf (for
discrete variables only),
Probability Density Function -
pdf (mainly for continuous variables), or
Cumulative Distribution Function - cdf (for either
discrete or continuous variables).
Probability mass function (pmf)
Suppose the discrete random variable
can take a set of
real values
, then the
pmf is defined as:
where
. e.g. For a normal 6-sided die,
and
. For a pair of dice being thrown,
and the pmf is as shown in (a) of
.
Cumulative distribution function (cdf)
The
cdf can describe discrete, continuous or
mixed distributions of
and is
defined as:
For discrete
:
giving step-like cdfs as in the example of (b) of
.
Properties follow directly from the Axioms of Probability:
,
is non-decreasing as
increases
where there is no ambiguity we will often drop the subscript
and refer to the cdf as
.
Probability density function (pdf)
The
pdf of
is
defined as the derivative of the cdf:
The pdf can also be interpreted in derivative form as
:
For a discrete random variable with pmf given by
:
An example of the pdf of the 2-dice discrete random process isshown in (c) of
.
(Strictly the delta functions should extend vertically toinfinity, but we show them only reaching the values of their
areas,
.)
The pdf and cdf of a continuous distribution (in this case the
normal or
Gaussian distribution) are
shown in (d) and (e) of
.
The cdf is the integral of the pdf and
should always go from zero to unity for a valid probabilitydistribution.
Properties of pdfs:
As for the cdf, we will often drop the subscript
and refer simply to
when no confusion can arise.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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