Question

In: Statistics and Probability

Determine whether the distribution is a discrete probability distribution. If not, state why.

Determine whether the distribution is a discrete probability distribution. If not, state why.

x

P(x)

0

0.1

1

0.5

2

0.05

3

0.25

4

0.1

Solutions

Expert Solution

Given distribution is in table form.

x 0 1 2 3 4
P(x) 0.1 0.5 0.05 0.25 0.1

Check whether the distribution is a discrete probability distribution.

To be a discrete probability distribution, we must have a numerical random variable \(x\) such that \(P(x)\) must satisfy the preceding three requirements.

1. The variable \(x\) is a discrete random variable and its values are associated with probabilities.

2. \(\sum P(x)=P(0)+P(1)+P(2)+P(3)+P(4)\)

\(=0.1+0.5+0.05+0.25+0.1\)

\(=1\)

3. Each value of \(P(x)\) is between 0 and 1 .

The given table is a discrete probability distribution because it satisfies the discrete probability distribution's three requirements.

 

Related Solutions

Discrete R.V and Probability Distribution
A new battery's voltage may be acceptable (A) or unacceptable (U). A certain ash-light requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 90% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested. (a) What is p(2), that is, P(Y = 2)? (b) What is p(3)? [Hint: There are two different outcomes that result in Y = 3.] (c) To have...
Discrete R.V and Probability Distribution
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X be the number of months between successive payments. The cdf of X is as follows: \( F(x)=\begin{cases} 0,\hspace{7mm} x < 1 & \quad \\ 0.10, \hspace{2mm}1\leq x < 3 & \quad \\ 0.40, \hspace{2mm}3 \leq x < 7 & \quad \\ 0.80, \hspace{2mm} 7 \leq x < 12 & \quad \\ 1,\hspace{7mm} 12 \leq x: & \quad \end{cases} \) (a)...
Discrete R.V and Probability Distribution
A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table. Calculate the probability of each of the following events. (a) At most three lines are in use. (b) Fewer than three lines are in use. (c) At least three lines are in use. (d) Between two and five lines, inclusive, are in use. (e) Between two and...
Discrete R.V and Probability Distribution
In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 5% of the time. Suppose that an auditor randomly checks three entries. (a) Find the probability distribution for X , the number of errors detected by the  auditor. (b) Find the probability that the auditor will detect more than one error.  
Discrete R.V and Probability Distribution
A problem in a test given to small children asks them to match each of three pictures of animals to the word identifying that animal. If a child assigns the three words at random to the three pictures ,Find the probability distribution for Y , the number of correct matches.
Discrete R.V and Probability Distribution
A group of four components is known to contain two defectives. An inspector tests the components one at a time until the two defectives are located. Let X denote the number of the test on which the second defective is found. Find the probability distribution for X.
Discrete R.V and Probability Distribution
An electronics store has received a shipment of 20 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other eight have a single slot. Suppose that six of the 20 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X= the number among the radios stored under the display...
Discrete R.V and Probability Distribution
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled holes. Five gearboxes must be selected from the 20 that are available for installationcin the next five robots. (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard...
Discrete R.V and Probability Distribution
A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 25 items are readied for shipment, and a sample of 3 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped. (a) What is the probability that a box containing 3 defectives will be shipped? (b) What...
Discrete R.V and Probability Distribution
Knowing that 80% of the volunteers donating blood in a clinic have type A blood. (a) If five volunteers are randomly selected, what is the probability that at least one does not have type A blood? (b) If five volunteers are randomly selected, what is the probability that at most four have type A blood? (c) What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT