***PLEASE ANSWER EVERY QUESTION AND BE VERY DETAILED!!!*** 1. What is a Non-Nega

Question

***PLEASE ANSWER EVERY QUESTION AND BE VERY DETAILED!!!***

1. What is a Non-Negative and a Unrestricted Distribution? Give an example of EACH

2. Give an example of Discrete Distribution, Symmetric Distribution, Skewed Distribution, Bounded Distribution, and Unbounded Distribution

3. What kind of distribution does min+(rand()*(max-min)) provide in Excel?

4. What does norminv(rand(),100,5) provide in Excel?

5. What is the flaw of averages? How would you avoid the issues of making decisions based on averages, or point estimates?   

Explanation / Answer

1).Non-Negative vs Unrestricted is a Special case of bounded distributions is when the only possible values are nonnegative.
In such cases, model the randomness with a probability distribution that is bounded below 0. Rules out non-negative numbers that make no sense.

Example"Uniform Probability Distribution:

The simplest probability distribution occurs when all of the values of a random variable occur with equal probability. This probability distribution is called the uniform distribution.

Uniform Distribution. Suppose the random variable X can assume k different values. Suppose also that the P(X = xk) is constant. Then,

P(X = xk) = 1/k

Example :

Suppose a die is tossed. What is the probability that the die will land on 5 ?

Solution: When a die is tossed, there are 6 possible outcomes represented by: S = { 1, 2, 3, 4, 5, 6 }. Each possible outcome is a random variable (X), and each outcome is equally likely to occur. Thus, we have a uniform distribution. Therefore, the P(X = 5) = 1/6.

2).Discrete Probability Distributions:

When we say that the probability distribution of an experiment is discrete then the sum of probabilities of all possible values of the random variable must be equal to 1. That is if X is a discrete random variable, then,

eP(X=e)=1

Here, ‘e’ is the set of all values that the variable X can take.

Example : Find the expected value of the following discrete distribution.

Y    P(Y) YP(Y)
0        0.30        0
1        0.20        0.20
2        0.25        0.50
3        0.15        0.45
4        0.10        0.40
So expected value = 0 + 0.20 + 0.50 + 0.45 + 0.40 = 1.55

Skewed Distribution: A skewed distribution is one which is not symmetrical about the mean, or average. An exponential distribution is one example of a skewed probability distribution.

Symmetric Distribution : A bell-shaped or mound-shaped curve or a normal distribution, is just one example of a shape that a distribution can take on. The normal distribution is an example of a symmetric distribution.

Bounded Distribution: A distribution that is confined to lie between two determined values is said to be bounded. Examples of bounded distributions are: Uniform - between minimum and maximum, Triangular - between minimum and maximum, Beta - between 0 and Scale , and Binomial - between 0 and n.

Unbounded Distribution:A distribution that is unbounded theoretically extends from minus infinity to plus infinity. Examples are: Normal, Logistic, and Extreme Value.

3).Uniform distribution.

Uniform Random Numbers - The Standard Excel Way:

The standard Excel RAND function can be used to generate random numbers from the Uniform distribution,

the RAND function returns numbers from the interval [0,1), and if you need to generate numbers from another interval, you should use the following formula:

=RAND() * (ba) + a

This will return random numbers from the interval [a,b) - greater than or equal to a, and less than b.   

where a=min and b=max

4).This function will generates a random variable which Returns the inverse of the normal cumulative distribution for the mean 100 and standard deviation 5.

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