Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

Suppose X and Y are jointly continuous with joint pdf f(x,y)=xe^[-x(1+y)], x,y>0. a) What are the marginal pdf's of X and Y? b) What is the conditional pdf of X given Y=y? c) What is the conditional pdf of Y given X=x? d) What is the distribution of Y given X=x called?

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

Suppose X and Y are continuous random variable, X and Y are independent and that x>0 and y>0. The pdf of X is Fx(X) and the pdf of Y is Fy(Y). Find the expressions for the density function of Z in terms of fx and fy, if... a) Z=X/Y b) Z=XY

Stat Class

#4. Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in the sample space? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type? d. Which outcomes are in the event that at most one of the four is a variable-rate mortgage? e. What is the union of the events in parts (c) and (d), and what is the intersection of these two events? f. What are the union and intersection of the two events in parts (b) and (c)?

Stat Class

#34. A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 45). a. How many selections result in all 6 workers coming from the day shift? What is the probability that all 6 selected workers will be from the day shift? b. What is the probability that all 6 selected workers will be from the same shift? c. What is the probability that at leas... click for more

Stat Class

#8. An engineering construction firm is currently working on power plants at three different sites. Let Ai denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1, A2, and A3, draw a Venn diagram, and shade the region corresponding to each one. a. Exactly one plant is completed by the contract date. b. Either the plant at site 1 or both of the other two plants are completed by the contract date. c. At least one plant is completed by the contract date.