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Chapter 4: Q4.1-4E (page 216)

Suppose that one word is to be selected at random from the sentence the girl put on her beautiful red hat. If X denotes the number of letters in the word that is selected, what is the value of E(X)?

Short Answer

Expert verified

The value \(E(X)\) is 3.75

Step by step solution

01

Given information

A sentence is given, and it consists of 8 words. The word is to be chosen at random, and it contains some letters as given below:

The probability of selecting a word is \(\frac{1}{8}\) as every word is equally likely to be selected. X is the random variable that denotes a word is chosen, and we are to compute \(E(X)\)

02

Compute \({\bf{E}}\left( {\bf{X}} \right)\)

\(\begin{array}{l}E(X) = \sum\limits_{x = 1}^8 {xP(X = x)} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sum\limits_{x = 1}^8 {x\,\frac{1}{8}} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{8}\left( {3 + 4 + 3 + 2 + 3 + 9 + 3 + 3} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3.75\end{array}\)

So, the value \(E(X)\) is 3.75

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