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Chapter 5: Problem 5

Briefly explain the two characteristics (conditions) of the probability distribution of a discrete random variable.

Short Answer

Expert verified
The two characteristics of a discrete random variable's probability distribution are: 1) Every individual probability is between 0 and 1, inclusive; and 2) The total sum of all probabilities equals to 1.

Step by step solution

01

Describe the Range of Probabilities

This is the first condition for a probability distribution. Each individual probability, or the likelihood of an outcome occurring, must be between 0 and 1 inclusive. This range indicates that an event is either impossible to occur (probability of 0), certain to occur (probability of 1), or somewhere in between.
02

Discuss the Sum of Probabilities

This is the second condition for a probability distribution. The total sum of all individual probabilities in the distribution must equal 1. This indicates that one of the possible outcomes must exactly occur.

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Most popular questions from this chapter

Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5 keyboards from that box. The shipment is accepted if not more than 1 of the 5 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 6 defective keyboards. a. What is the probability that this shipment will be accepted? b. What is the probability that this shipment will not be accepted?

Twenty percent of the cars passing through a school zone are exceeding the speed limit by more than \(10 \mathrm{mph}\). a. Using the Poisson formula, find the probability that in a random sample of 100 cars passing through this school zone, exactly 25 will exceed the speed limit by more than \(10 \mathrm{mph}\). b. Using the Poisson probabilities table, find the probability that the number of cars exceeding the speed limit by more than 10 mph in a random sample of 100 cars passing through this school zone is i. at most 8 ii. 15 to 20 iii. at least 30

What are the conditions that must be satisfied to apply the Poisson probability distribution?

Let \(N=11, r=4\), and \(n=4\). Using the hypergeometric probability distribution formula, find a. \(P(2)\) b. \(P(4)\) c. \(P(x \leq 1)\)

Let \(x\) be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of \(x\) for each of the following. Find the mean, variance, and standard deviation for each of these probability distributions. Draw a graph for each of these probability distributions. a. \(\lambda=1.3\) b. \(\lambda=2.1\)
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