Required information In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06 Find the marginal probability mass function px(x). (Round the final answer to two decimal places.) PX(0)| PX(1) PX(2)

Consider rolling 2, 3-sided dice. Let X = the sum of the dice. Let Y = the product of the dice. a. Find the joint probability function for X and Y. b. Find the marginal probability functions for X and Y. Find P(X > 3|Y = 3) C.

Required information In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06 Find P(X= 1 and Y=0). (Round the final answer to two decimal places.)

The probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.84 and 1.3 is:

Grade A B U Frequency 5 a 9 7 D ** F 5 Refer to the table. Given that receiving at least a C is passing the course, calculate the probability a student passed the course.

Fill this table with the missing columns: Interval Frequency Probability Probability Density 1 3 13 4 - 6 15 7-9 19 9 - 11 14 11-16 17 - 26 3

In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: y 0.10 0.11 0.05 0.17 0.23 0.08 2 0.06 0.14 0.06 Find P(X = land Y = 0). a. Find P(X 2 land Y 1). b. C. d. Find the probability that the standard for ozone is exceeded at least once. Find the probability that the standard for particulate matter is never exceeded. e. f. Find the probability that neither standard is ever exceeded. g.

Match the appropriate probability distribution functions shown in column B with the statistic present in column A drawn from a normally distributed population.   Statistic Probability Distribution Sample Mean, Known population mean population standard deviation F distribution Sample Mean, Known population mean unknown population standard deviation Chi-square distribution Sample standard deviation Student “t”- distribution Ration of Sample Standard deviations Normal Distribution