|(a) Var(X + 3)
(b) E(7X + 5Z)
(c) E(1 / X²)
(f) E(Y Z)
|(g) E(X Y)
(h) E(Y / Z)
(a) Approximate P(Xav <8).
(b) Let Y1,Y2, Y3, . . . Y50 be a random sample from a distribution with mean 0 and variance 1. Let Yav be the average of the 50 Y's. What is the approximate distribution of Xav + Yav ?
|(a)||What is the probability that a Revenue Canada auditor will catch only two income tax returns with illegitimate deductions if she randomly selects five returns from among 15 returns of which 9 contain illegitimate deductions?|
|(b)||In the inspection of a fabric produced in continuous rolls the number of imperfections per ten yards is a random variable having a Poisson distribution with lambda=2.8. Find the probability that ten yards of the fabric will have at most three imperfections.|
|(c)||If 40% of the mice used in an experiment will become very aggressive within one minute after having been administered an experimental drug, find the probability that exactly six of the fifteen mice which have been administered the drug will become very aggressive within one minute.|
|(d)||The probability that a newborn child will be male is about 52%. If a large hospital has 1290 live births in a given year, what is the probability that 700 or more of the babies born during this year at this hospital will be male?|
|(e)||The probability that a salmon caught in the Ottawa River will be of a suitable size to be kept, according to game regulations, is 0.08. What is the probability that an individual will have to catch more than 9 fish to be able to keep one?|