Chapter 6.1, Problem 3E

a.

To determine

To interpret: The event in terms of X and compute the probability of this event.

Answer to Problem 3E

The probability is 0.9.

Explanation of Solution

Given:

The probability distribution is:

Value of X	0	1	2	3	4
Probability	0.1	0.2	0.3	0.3	0.1

Calculation:

Consider, X be the random variable that shows the number of nonword errors. The at least non-word error could be written as $X\ge 1$ .

The probability is computed as:

  $\begin{array}{c}P\left(X\ge 1\right)=1-P\left(X<1\right)\\ =1-P\left(X=0\right)\\ =1-0.1\\ =0.9\end{array}$

The probability is 0.9.

b.

To determine

To explain: The event $X\le 2$ in words. Also, compute the probabilities for $X\le 2$ and $X<2$

Answer to Problem 3E

The probabilities are 0.6 and 0.3.

Explanation of Solution

Calculation:

  $X\le 2$ means that the non-word errors are 2 or less.

The probabilities could be calculated as:

  $\begin{array}{c}P\left(X\le 2\right)=P\left(X=0\right)+P\left(X=1\right)+P\left(X=2\right)\\ =0.1+0.2+0.3\\ =0.6\end{array}$

Now,

  $\begin{array}{c}P\left(X<2\right)=P\left(X=0\right)+P\left(X=1\right)\\ =0.1+0.2\\ =0.3\end{array}$

Thus, the probabilities are 0.6 and 0.3 respectively.