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

        “A singlelink flexible arm is a dynamic system with the first eigenvalueequal to zero and giving the primary rigid body motion and theeigenvalues greater than zero giving flexural vibration that mayoccur during the response. The object is to drive the arm tip to aconstant steady state position in as fast a time as possible whilekeeping the arm tip vibration to a minimum.”

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

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

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

(C)    Determine the mean μ and standarddeviation σ.

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

           μ-σ and μ+σ.

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