Question

. Consider the 68 words in the following two sentences to be modeled as random variables. The sentences contain words of 1 letter length to 10 letter length. Thus random variable x lies in the range 1 ≤ x ≤ 11

        “A single link flexible arm is a dynamic system with the first eigenvalue equal to zero and giving the primary rigid body motion and the eigenvalues greater than zero giving flexural vibration that may occur during the response. The object is to drive the arm tip to a constant steady state position in as fast a time as possible while keeping the arm tip vibration to a minimum.”

(A) Develop a bar graph for the number of words with a specific number of letters.

For example, in the phrase “This is an example for the type of words related to this problem”:   3 two letter words, 2 three letter words, 3 four letter words, 1 five letter word, 3 seven letter words.

(B) Calculate the probability density distribution and show it bar form. Use 1 for the transition from probability to probability density which makes these two the same.

(C)    Determine the mean μ and standard deviation σ.

(D)   Use part B result and determine the probability that a word falls between

            μ-σ and μ+σ.

   (E) If the system is modeled with a continuous normal probability distribution, determine the probability that a word falls between 6 and 9 letters.

Answer 1

A)

B)

C)

D)

Mu-sigma	2.146607765
Mu+sigma	6.941627529

We can calculate approximatedly by adding probabilities P(2.14 <= X <= 6.94) = 0.7794