Find the expected values of the random variables X and Y if
P(X = 0) = 1/ 2 , P(X = 1) = 1/ 2 , P(Y = 1) = 1/ 4 , and P(Y = 2) = 3/ 4 .
Compare E(X) + E(Y ) with E(X +Y ) , if
P(X = x,Y = y) = P(X = x)P(Y = y) . (10%)
A college officer wants to estimate the proportion of students who favor a
new policy in a college. Suppose there are only two possible answers, i.e.,
“yes” or “no”, for the survey. The estimate is to be within 0.05 of the true
proportion favoring the new policy, with a 90% confidence coefficient.
Determine the largest sample size necessary to ensure the desired results.
( z0.05 = 1.645 , z0.025 = 1.96 ) (10%)
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