Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. Let Z = X + Y represent the total number of repairs needed. The joint probability mass function of X and Y is as follows:   y x 0 1 2 3 0 0.13 0.10 0.07 0.03 1 0.12 0.16 0.08 0.04 2 0.02 0.06 0.08 0.04 3 0.01 0.02 0.02 0.02     Find σZ.. (Round the final answer to three decimal places.)

Given a die in the shape of a regular octahedron, find the probability that one roll produces a an even- number result b a result of 4 or more.

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.

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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 x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06 Find Cov(X, Y). (Round the final answer to four decimal places.) Find ρX,Y. (Round the final answer to four decimal places.)

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 x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06   Find P(X < 1). (Round the final answer to two decimal places.) Find the probability that the standard for ozone is exceeded at least once. (Round the final answer to two decimal places.) Find the probability that the standard for particulate matter is never exceeded. (Round the final answer to two decimal places.)Find the probability that neither standard is ever exceeded. (Round the final answer to two decimal places.)

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 x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06     Find the conditional probability mass function pX|Y(x|1). (Round the final answer to four decimal places.) The value of pX|Y(0|1) is  . The value of pX|Y(1|1) is  . The value of pX|Y(2|1) is  . Find the conditional expectation E(Y|X = 0). (Round the final answer to four decimal places.) Find the conditional expectation E(X|Y = 1). (Round the final answer to four decimal places.)

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 x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06   1. Find the conditional probability mass function of pY|X(y|0). (Round the final answer to four decimal places.) The value of pY|X(0|0)  The value of pY|X(1|0) The value of pY|X(2|0)    2.  Find the conditional probability mass function pX|Y(x|1). (Round the final answer to four decimal places.) The value of pX|Y(0|1)  The value of pX|Y(1|1)  The value of pX|Y(2|1)    3. Find the conditional expectation E(Y|X = 0). (Round the final answer to four decimal places.) The value of…

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       x 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06     Find the conditional probability mass function of pY|X(y|0). (Round the final answer to four decimal places.)   The value of pY|X(0|0) is :   The value of pY|X(1|0) is :   The value of pY|X(2|0) is :

Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: a. What is the value of C? b. Find the marginal probability mass function . c. Find the marginal probability mass function . d. Find u_x . e. Find  u_y. f. Find sigma_x. g. Find  sigma_y. h. Find  cov(x,y). i.  Find rho_xy. j.  E[X+Y] k.  VAR[X+Y] l.  Are X and Y independent? Explain. m.  What is the CDF Fx(x)? n.  What is the CDF Fy(y)?