Question

Give an example of a real life event that would occur as a discrete random variable. Discuss why would it be valuable to estimate the probability of such an event occurring.

Answer #1

An example of discrete random variable would be the probabilities of recieving number of calls(say 0 to 10) by a customer care executive in one hour in a day.

Suppose we are operating a call centre, based on the probabilities of number of calls it can be identified whether there is a requirement of more customer care executives or less or the present number is sufficient. Thus, these probabilities of discrete number of calls would help us to forecast the expected number of calls and hence help us to find number of executives required in the centre.

Using a real life example explain where the formula for
conditional probability [P(B|A) = P(A ∩B) P(A) ] comes from. Hence,
or otherwise, explain why, for independent events, the probability
of the two events both occurring is the same as the probability of
the first event occurring multiplied by the second event
occurring.

Consider an event that will either occur or not. For example, the
event might be that California will experience a major earthquake
in the next five years. You let p be the probability that the event
will occur. Does it make any sense to have a probability
distribution of p? Why or why not? If so, what might this
distribution look like? How would you interpret it?

What is the difference between a continuous random variable and
a discrete random variable? In your own words, do not copy from the
internet. Please also give an example.

Please discuss the applications of timers. Give an example in
real life (both commercial and industrial).

Why we need multivariate random variables and give real life
correlated multivariate random variables.

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

Suppose that X is a discrete random variable with ?(? = 1) = ?
and ?(? = 2) = 1 − ?. Three independent observations of X are made:
(?1, ?2, ?3) = (1,2,2).
a. Estimate ? through the sample mean (this is an example of the
“method of moment” for estimating a parameter).
b. Find the likelihood function and MLE for ?.

What kind of variable has values determined by chance?
random variable
discrete variable
continuous variable
Question 5
A binomial distribution is a probability distribution for a:
discrete random variable
continuous random variable
Question 6
A normal distribution is a probability distribution for a:
continuous random variable
discrete random variable
Question 7
Which is not a property of the binomial distribution?
only two outcomes
fixed number of trials
constant probability of success
dependent outcomes

Give your own example of a stochastic process that is discrete
state space and discrete time. Explain why this process fits this
category.

Question 1 has two parts:
Give an example (real or fictional) of a news event that would
shift aggregate demand, ceteris paribus. In the interim between
just before the event occuring to its final outcome (in the short
run), describe what is happening to real GDP, the unemployment
rate, and the inflation rate.
Give an example (real or fictional) of a news event that would
shift the aggregate supply curve in the short-run, ceteris paribus.
In the interim between just...

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