Exam 5: Discrete Random Variables

Find the specified probability. -There are only 8 chairs in our whole house. Whenever there is a party some people have no where to sit. The number of people at our parties (call it the random variable X)changes with each party. Past records show that the probability distribution of X is as shown in the following table. Find the Probability that everyone will have a place to sit at our next party. 5 6 7 8 9 10 >10 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

Evaluate the expression. - $\left( \begin{array} { c } 11 \\ 3 \end{array} \right)$

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. -A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with parameter $\lambda$ = 4.1. Find the probability that on a randomly selected trip, The number of whales seen is

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. -In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda$ = 4.7 Find the probability that in a randomly selected week the number of burglaries is at least three.

Determine the possible values of the random variable. -For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. What are the possible values of the random variable Y?

Determine the binomial probability formula given the number of trials and the success probability for Bernoulli trials.Let X denote the total number of successes. Round to three decimal places. - $\mathrm { n } = 5 , \mathrm { p } = 0.6 , \mathrm { P } ( \mathrm { X } = 2 )$

Evaluate the expression. - $\frac { 9 ! } { 7 ! }$

Use random-variable notation to represent the event. -Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. Use random-variable notation to represent the event that the total number of tails is three.

Which of the following describes the possible values of a Poisson random variable, X?

Find the indicated probability. Round to four decimal places. -A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 21 components and accept the whole batch if there are fewer than 3 Defectives. If a particular shipment of thousands of components actually has a 3% rate of defects, What is the probability that this whole shipment will be accepted?

Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places. -The rate of defects among CD players of a certain brand is 1.4%. Use the Poisson approximation to the binomial distribution to find the probability that among 230 such CD players received by a Store, there is at most one defective.

Construct the requested histogram. -Each person from a group of recently graduated math majors revealed the number of job offers that he or she had received prior to graduation. The compiled data are represented in the table. Construct the probability histogram for the number of job offers received by a graduate randomly Selected from this group. Number of offers 0 1 2 3 4 Frequency 4 10 25 5 6

Calculate the specified probability -Suppose that $\mathrm { K }$ is a random variable. Given that $\mathrm { P } ( - 3.45 \leq \mathrm { K } \leq 3.45 ) = 0.35$ , and that $\mathrm { P } ( \mathrm { K } < - 3.45 ) =$ $P ( K > 3.45 )$ , find $P ( K > 3.45 )$ .

Find the specified probability. -Use the special addition rule and the following probability distribution to determine $P ( X \geq 8 )$ . 5 6 7 8 9 10 11 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

A Poisson random variable has an infinite number of possible values?

Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games?

A coin is biased so that the probability it will come up tails is 0.43. The coin is tossed three times. Considering a success to be tails, formulate the process of observing the outcome of the three tosses as a sequence of three Bernoulli trials. Complete the table below by showing each possible outcome together with its probability. Display the probabilities to three decimal places. List the outcomes in which exactly two of the three tosses are tails. Without using the binomial probability formula, find the probability that exactly two of the three tosses are tails. Outcome Probability hhh (0.57)(0.57)(0.57)=0.185

40% of the adult residents of a certain city own their own home. Four residents are selected at random from the city and asked whether or not they own their own home. Considering a success to be "owns their own home", formulate the process of observing whether each of the four residents owns their own home as a sequence of four Bernoulli trials. Complete the table below by showing each possible outcome together with its probability. Display the probabilities to three decimal places. List the outcomes in which exactly two of the four residents own their own home. Without using the binomial probability formula, find the probability that exactly two of the four residents own their own home. Outcome Probability ssss (0.4)(0.4)(0.4)(0.4)=0.026

Evaluate the expression. -10!

Construct the requested histogram. -If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H)and tails (T). Suppose the random variable X represents the number of heads in a sequence. Construct the probability Distribution for X.