Online Notes PDF

Preview

Summary

Just some online notes useful stuff from the online textbook and assignments on MyStatLab...

Description

5.3 Two events are disjoint if they have no outcomes in common. In other words, the events are disjoint if, knowing that one of the events occurs, we know the other event did not occur. Independence means that one event occurring does not affect the probability of the other event occurring. Therefore, knowing two events are disjoint means that the events are not independent.

The notation P(F|E) is read “the probability of event F given event E.” It is the conditional probability that event F occurs, given that event E has occurred.

Conditional Probability Rule If

E and F are any two events, then P(F|E)=P(E and F)P(E)=N(E and F)N(E)

The probability of event

F occurring, given the occurrence of event E, is found by

dividing the probability of outcomes in

E and F by the probability of E, or by dividing the number of

E and F by the number of outcomes in E.

6.1 A continuous variable is a quantitative variable that has an infinite number of possible values that are not countable and a discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. A continuous variable may take on every possible value between any two values, while a discrete variable cannot.

The probability distribution of a discrete random variable X provides the possible values of the random variable and their corresponding probabilities. A probability distribution can be in the form of a table, graph, or mathematical formula. In the graph of a discrete probability distribution, the horizontal axis is the value of the discrete random variable and the vertical axis is the corresponding probability of the discrete random variable. When graphing a discrete probability distribution, we want to emphasize that the data are discrete. Therefore, draw the graph of discrete probability distributions using vertical lines above each value of the random variable to a height that is the probability of the random variable. EX

Suppose a life insurance company sells a $240,000 one year term life insurance policy to a 25-year old female for $210. The probability that the female survives

the year is .999592. Compute the expected value of this policy to the insurance company.

($210)(0.999592)−($239790)(0.000408)

==== ANSWER...