Question

how are continuous random variables used in industry research, academic research, and scientific research.

Answer #1

The normal distribution is the most widely used probability distribution in world, which is a continuous distribution.

Continuous distribution: Every real number in the range has a probability.

Example of industrial use:

Surface roughness measurement of a component involves normal distribution. A component is accepted when it is very near to optimum roughness not more not less. Obtained roughness values, not integers they are continuous outcomes.

Example of academic research:

Percentage of performance of students in an institute is always continuous. It is having real values and for each real value, there is a probability of occurrence.

Example of scientific research:

The amount of radioactive uranium 235 needed to start a nuclear reaction. For every amount, there is a probability of nuclear reaction.

Include a paragraph explaining how human cadavers are used in
today's society to further scientific research.

Which of the following statements about continuous random
variables and continuous probability distributions is/are TRUE?
I. The probability that a continuous random variable takes a
specific value is 0.
II. The probability that a continuous random variable takes a
negative value is 0.
III. The probability that any uniformly distributed random
variable takes a value less than its mean is 0.5.
IV. The probability that a normally distributed random variable
takes a value less than its mean is 0.5.

Which of the following random variables are
continuous?
The time that an individual spend talking on their phones
during a given week.
The number of 911 calls responded daily by the NYC police
The daily rentals rates for luxury cars in the US
Provide your own examples of at least 2 more continuous
variables and explain why they are continuous.

provide some examples of discrete and continuous random variables
in a quality management context.

A consequence of continuous random variables having an infinite,
uncountable set of possible values is that the probability of any
continuous random variable that equals to a specific value is
always ______________.
Multiple Choice
zero
very hard to tell
an extremely small number
less than one

Respond to these questions:
• Explain what dummy variables are and how they can be used to
account for seasonality.
• Please cite at least one academic article (APA or MLA
format).
• Select a product or service of your choice and explain how you
would use dummy variables to measure seasonality in the sales of
that product or service.
• Explain the expected sign of each dummy variable.

Let X and Y be two continuous random variables with joint
probability density function
?(?, ?) = { ? 2 + ?? 3 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 2 0 ??ℎ??????
Find ?(? + ? ≥ 1). Sketch the surface in the ? − ? plane.

How would you synthesize research in an academic article into
digestible information that practitioners can apply in their
organizations?

. X,Y are absolutely continuous, independent random variables
such that P(X ≥ z) = P(Y ≥ z) = e−z for z ≥ 0. Find the expectation
of min(X,Y )

A study in the Journal of Leisure Research investigated the
relationship between academic performance and leisure activities.
Each in a sample of 159 high school students was asked to state how
many leisure activities they participated in weekly. From the list,
activities that involved reading, writing, or arithmetic were
labeled "academic leisure activities." Some of the results are
listed below:
Mean
Standard Deviation
GPA
2.96
0.71
Number of leisure activities
12.38
5.07
Number of academic
leisure activities
2.77
1.97
Knowing...

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