the table below is a joint probability table that display the joint probablitly distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left turn lane. based on the data below what is the expected total number of cars and Busses E(X+Y) per cycle? p(x,y) Y 0 1 2 X 0 .025 .015 .010 1 .050 .030 .020 2 .125 .075 .050 3 .150 .090 .060 4 .100 .060 .040 5 .050 .30 .020

In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 5% of the time. Suppose that an auditor randomly checks three entries. a Find the probability distribution for Y, the number of errors detected by the auditor. b Construct a probability histogram for p(y). C Find the probability that the auditor will detect more than one error.

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was  μ = 9.1 mg/L  with 95% of the data ranging from 6.7 mg/L to 11.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal.   QUESTION: (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.)

Let X be the discrete r.v. that represents the number of Boys in a three-child family. Assume that the outcomes boys and girls are equally likely. What is the expected value of this discrete probability distribution?  What is the variance?

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was  μ = 9.9 mg/L  with 95% of the data ranging from 7.3 mg/L to 12.5 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand.

Suppose we are interested in the relationship between an individual's brown hair and skin color. Based on a random sample of LIU students, we have the following joint probability distribution given by: X-degree of brown hair color 2 3 4 0.12 0.01 0.05 0.07 0.07 0.12 0.09 0.16 Y- degree of skin color 2 0.12 3 0.16 | 0.03 The probability that an individual with degree of brown hair 2 has a degree of skin color 1 is: None of these 0.263 0.167 0.3

A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was  μ = 9.2 mg/L  with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand.   (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.)   (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.8 mg/L with 95% of the data ranging from 6.6 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) 0.7734 (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…

The average amount of time until a car accident on a particular 60 mile stretch of road is 30 minutes. Assume(unreasonably) that car accidents are independent, the time to a car accident is exponentially distributed, and that two accidents cannot occur at the same time. a. What is the probability of a car accident occurring in the first hour?b. What is the probability of a car accident occurring between 15 and 45 minutes? c. What is the variance of the time until a car accident occurs? If a car accident has not happened in 2 hours, what is the probability it will happen in the next hour?   DO NOT USE THE INTEGRATION METHOD PLEASE.