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Chapter 4: Q10. (page 217)

Stock market. Give an example of a continuous random variable that would be of interest to a stockbroker.

Short Answer

Expert verified

Example: The time taken by a stockbroker for the completion of the transactions of the stocks.

Step by step solution

01

Elucidating the continuous random variables

The continuous random variables are those variables that take infinite values for which it is very difficult to count by anyone. The values of continuous random variables can fluctuate a lot.

02

Specifying the example of the continuous random variables

The time taken for the completion of the transaction of stocks between two market participants through a stockbroker varies a lot. The variation in time depends upon the situation and the momentum of change in the stock prices, which means that it can take infinite values.

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Most popular questions from this chapter

Find a value of the standard normal random variable z, call itz0 such that

a.P(-z0鈮�z鈮�z0)=.98b.P(z鈮�z0)=.05c.P(z鈮�z0)=.70d.P(z鈮�z0)=.025e.P(z鈮�z0)=.70

4.133 Suppose xis a random variable best described by a uniform

probability distribution with c= 20 and d= 45.

a. Find f(x)

b. Find the mean and standard deviation of x.

c. Graph f (x) and locate 渭and the interval 渭卤2蟽onthe graph. Note that the probability that xassumes avalue within the interval 渭卤2蟽is equal to 1.

Reliability of a manufacturing network. A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit (IC) cards with two production lines set up in sequence. Items (IC cards) first pass through Line 1, then are processed by Line 2. The probability distribution of the maximum capacity level (x) of each line is shown below. Assume the lines operate independently.

a. Verify that the properties of discrete probability distributions are satisfied for each line in the system.

b. Find the probability that the maximum capacity level for Line 1 will exceed 30 items.

c. Repeat part b for Line 2.

d. Now consider the network of two production lines. What is the probability that a maximum capacity level exceeding 30 items is maintained throughout the network? [Hint: Apply the multiplicative law of probability for independent events.]

e. Find the mean maximum capacity for each line. Interpret the results practically.

f. Find the standard deviation of the maximum capacity for each line. Then, give an interval for each line that will contain the maximum capacity with probability of at least .75.

Find the following probabilities for the standard normal

random variable z:

a.P(z鈮�2.1)

b.P(z鈮�2.1)

c.P(z鈮�-1.65)

d.P(-2.13鈮�z鈮�-.41)

e.P(-1.45鈮�z鈮�2.15)

f.P(z鈮�-1.43)

Given that x is a Hypergeometric random variable with N=10, n=5, and r=6, compute the following:

a. P(X=0)

b. P(x=1)

c. P(X猢�1)

d. P(X猢�2)
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