## Related questions with answers

An office has four copying machines, and the random variable $X$ measures how many of them are in use at a particular moment in time. Suppose that $P(X = 0) = 0.08\,, \,P(X = 1) = 0.11\,,\, P(X = 2) = 0.27\,,\,$ and $P(X = 3) = 0.33$ . $\mathbf{(a)}$What is $P(X=4) ?$ $\mathbf{(b)}$ Draw a line graph of the probability mass function. $\mathbf{(c)}$ Construct and plot the cumulative distribution function.

Solution

Verified$\underline{\color{#4257b2}{\textbf{ Probability Mass Function ( Distribution ) }}}$

$\color{#4257b2}{ \text{Let } X \text{ be a discrete random variable and } \underline{P(X = x_i) = p_i}} .$

$\color{#4257b2}{ \text{The } \text {probability mass function (p.m.f.) } \text{of } X \text { is a set of probability values } pi \text{ , and} }$

$\color{#4257b2}{\text{these probability values must satisfy two conditions : }}$

$\begin{align*} \color{#4257b2}{(1) \,\,\,0 \le p_i \le 1}\\ \\ \color{#4257b2}{(2)\,\,\, \sum_i p_i =1} \end{align*}$

$\underline{\color{#4257b2}{\textbf{Cumulative Distribution Function }}}$

$\color{#4257b2}{ \text{The cumulative distribution function (c.d.f.) of } X \text{ is the function } }$

$\color{#4257b2}{\,\,\,F(x)=P(X \le x)}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Probability and Statistics for Engineers and Scientists

9th Edition•ISBN: 9780321629111 (4 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers#### Applied Statistics and Probability for Engineers

5th Edition•ISBN: 9780470053041Douglas C. Montgomery, George C. Runger#### Probability and Statistics for Engineers and Scientists

4th Edition•ISBN: 9781111827045 (2 more)Anthony J. Hayter#### Applied Statistics and Probability for Engineers

6th Edition•ISBN: 9781118539712 (1 more)Douglas C. Montgomery, George C. Runger## More related questions

1/4

1/7