Question

Create your own Binomial Probability RV and Distribution

1. Describe your Binomial Experiment. Choose an n of between 20 and 100:

2. Success = __________________________   Failure = _____________________________

3. X ~ _____ (______, ______)

4. List or give the range of the values that X takes on:

5. Give the PDF formula for the RV:

6. Find the expected value and standard deviation for your random variable.  

7. Write the probability questions described below about YOUR binomial RV and evaluate the probabilities.

a. A probability that X = a single value

b. A probability with “at most”

d. A probability with “more than”

e. A probability with "between"

Answer 1

1. Choose n = 25

2. Choose:

Success = p = 0.75

Failure = q = 0.25

3.

X B (25,0.75)

4. Range of the values that X takes on:

0 to 5

5.

PDF formula for the RV:

,

                  x = 0,1,2,,..,n

Substituting values, we get:

,

                            x = 0,1,2,...,25

6.

Expected value = E(x) = np = 25 X 0.75 = 18.75

Standard deviation = =

7.

(a) Let "single value" = 10

(b)

Let "at most" 2

P(X2) = P(X = 0) + P(X=1) + P(X=2)

So,

P(at most 2) = 0.0000

(d)

Let "more than" 2:

P(X>2) = 1 - P(X2) = 1 - 0.0000 = 1

(e) Let "between" 0 and 2:

So,

P(between 0 & 2) = 0.0000