Excel and Equations

BA501 : The Class : Stats : Discrete : Excel and Equations
Discrete Distributions- Excel and Equations
Excel

§ Excel and Equations §

Excel- commands used in this topic (Excel in Office 97 and Office 2000)

§ Frequency Distributions §

§ Poisson Distribution §

§ Equations §

Excel Steps

Frequency Distributions

(1) Use the steps to get a histogram. The frequency distribution will be a part of that output. Click on Tools-Data Analysis-Histograms. If Data Analysis does not show up, then click on Tools-Addins and select the top two options of Analysis Pack and Analysis Pack VBA.

(2) Create Bin value equal to the upper class limit (UCL) of each class. Highlight the cells next to the Bin values plus one cell. Click Paste-Function-Statistical-Frequency. Fill in the arrays in the box. While the box is still opend press Control-Shift-Enter.

Poisson Distribution

Click the Paste Function-Statistical-Poisson

Discrete Probability

Equations

Discrete Probability Equations used at this web site

§ Probability §

§ Discrete random variable § Population Mean §

§ Conceptual Variance and Standard Deviation §

§ Computing Variance and Standard Deviation §

§ Poisson PMF § Other Discrete Probability Equations §

§ Other Probability and Counting Rules §

1. Probability

Probability of event A = P(A) = m / n

where,

(a) The ratio m / n is a relative frequency.

(b) m = total number of times a single outcome occurs in an experiment

(c) n = total number of outcomes possible in an experiment

2. Discrete random variable.

X (random variable) = x₁ with P(x₁) or

= x₂ with P(x₂) or

= ... or

= x_n with P(x_n)

n = the number of possible outcomes in the experiment.

0 Ł P(x_n) Ł 1

SP(x_n) = 1

3. Population Mean

The population mean for any discrete probability distribution:

m = Sx_iP[x_i]

4. Conceptual Variance and Standard Deviation

Conceptual formulae for the variance and standard deviation for any discrete probability distribution:

(a) variance

s˛ = S[x_i - m]˛( P[x_i] ) (do not use for hand calculations)

(b) standard deviation

s = Ös˛ = Ö(S[x_i - m]˛( P[x_i] ) (do not use for hand calculations)

5. Computing Variance and Standard Deviation

Computing formulae for the variance and standard deviation for any discrete probability distribution:

(a) variance

s˛ = Sx_i˛P[x_i] - m˛ ( use for hand calculations)

(b) standard deviation

s = Ös˛ = Ö (Sx_i˛P[x_i] - m˛) ( use for hand calculations)

6. Poisson PMF

P[x] = [m^x][e^-^m] / x! (Do not use for hand calculations. Use table.)

where x = expected number of occurrences over time

and e = 2.71828...

(a) m = Sx_iP[x_i]

(b) s˛ = Sx_i˛P[x_i] - m˛

(c) m = s˛

Other Discrete Probability Equations not covered at this web site

§ Binomial PMF § Hypergeometric PMF §
§ Other Probability and Counting Rules §

1. Binomial PMF:

P[x_i] = _nC_x(p^x)(1 - p)^{(n
- x)}

n = # trials)

x = # of success = # tails

p = probability of success

_nC_x = n! / [x!(n - x)!]

2. For the Binomial Random Variable:

(a) Binomial Mean

m = Sx_iP[x_i] = n( p )

(b) Binomial Variance

s˛ = Sx_i˛P[x_i] - m˛ = n( p )[1 - p]

n = # trials)

x = # of success = # tails

p = probability of success

3. Hypergeometric PMF:

P[x] = {[_kC_x][ _{(N - k)}C_{(n - x)} ]} / _NC_n

(a) _kC_x is the number of successes, x out of k possible successes.

(b) _{N - k)}C_{(n - x)} is the number of failures ( n - x ) out of ( N - k) possible failures.

(c) _NC_n is the number of samples n out of a finite population size N.

<####) Mean

m = Sx_iP[x_i] = nk / N

(e) Variance

s˛ = Sx_i˛P[x_i] - m˛

= [n(k/n)(1- {k/N})] x [( N - n )/( N - 1)]

where[(N - n)/(N - 1)] = the finite population correction (fpc) factor

Other Probability and Counting Rules not covered at this topic site

§ Complement of an Event § Additive Rule §

§ Mutually Exclusive § Multiplicative Rule §

§ Independent Events § Rules for Conditionals § Counting Rules §

§ Combinations and Samples from a Population §

1. Complement of an Event:

P(A) + P(notA) = 1

P(A) = 1 - P(notA)

P( notA) = 1 - P(A)

2. Additive Rule:

The "or" probability (union)

P[A or B] = P(A) + P(B) - P(A & B)

3. Special Case of the Additive Rule:

Mutually Exclusive

P[A or B] = P(A) + P(B)

4. Multiplicative Rule:

The "and" probability (intersection)

P[A & B] = P[ A | B ]P[B]

= P[ B | A ]P[A]

5. Special Case of the Multiplicative Rule:

Independent Events

P[A|B] = P[ A ]

P[B|A] = P[ B ]

P[A & B] = P[ A ]P[ B]

6. Rules for Conditionals:

P[A | B] = P[ A & B ] / P[ B ], for P[B] > 0

P[B | A] = P[ A & B ] / P[ A ], for P[A] > 0

7. Counting Rules:

(a) Filling Slots k different independent slots. (Counting Rule # 1)

(n₁)(n₂)(...)(n_k)

(b) Permutations (Counting Rule # 2):

_nP_k = [n!] / [n - k]! = (n)(n - 1)(n - 2)(...)(n - k - 1)

n is the total number of objects

k is the number of objects selected

Used when order is important.

(c) Combinations (Counting Rule # 3):

_nC_k = [ _nP_k] / k! = [n!] / [k!][n - k]!]

n is the total number of objects

k is the number of objects selected

Used when order is not important.

8. The total numberof samples possible of size n, selected without replacement from a population size N is:

Combinations and Samples from a Population

_NC_n = [N!] / [n!][N - n]!,

probability of any one sample selected 1 / _NC_n

You should now:

Go on to Home Work
or
Go back to Discrete Distributions: Activities and Assignments

Please reference "BA501 (your last name) Assignment name and number" in the subject line of either below.

E-mail Dr. James V. Pinto at BA501@mail.cba.nau.edu
or call (928) 523-7356. Use WebMail for attachments.