suppose that you are looking for a student who lives within five miles of you.you know that 55% of the 25000 students do live wthin five miles of you.you randomly contact student s from the collage until one says he or she lives within five of you.give a probabiltity for this situation.using the probability modal find the probability that you need to contact four people.what can you say about the nature of the distribution?give measure
Answers
Step-by-step explanation:
Read this as "Xis a random variable with ageometric distribution." The parameter isp;p= the probability of a successfor each trial.The Geometric Pdf tells us the probability that the first occurrence of success requires x number of independent trials, eachwith success probability p. If the probability of success on each trial isp, then the probability that thexth trial (out of xtrials) is the first success isP⎛⎝X=x⎞⎠=⎛⎝1 -p⎞⎠x- 1pforx= 1, 2, 3, ....The above form of the Geometric distribution is used for modeling the number of trials until the first success. By contrast,the following form of the geometric distribution is used for modeling number of failures until the first success:P⎛⎝Y=x⎞⎠=⎛⎝1 -p⎞⎠xpforx= 0, 1, 2, 3, ....In either case, the sequence of probabilities is a geometric sequence.Example 4.8Assume that the probability of a defective computer component is 0.02. Components are randomly selected. Findthe probability that the first defect is caused by the seventh component tested. How many components do youexpect to test until one is found to be defective?LetX= the number of computer components tested until the first defect is found.Xtakes on the values 1, 2, 3, ... wherep= 0.02.X~ G(0.02)FindP(x= 7). Answer:P(x= 7) = (1 - 0.02)7-1× 0.02 = 0.0177.The probability that the seventh component is the first defect is 0.0177.The graph ofX~ G(0.02) is:194Chapter 4 | Discrete Random VariablesThis content is available for free at
Figure 4.2They-axis contains the probability ofx, whereX= the number of computer components tested.