We were given the following joint probabiltiy density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide:

f(y1,y2)={2, 0<=y1<=1, 0<=y2<=1, 0<=y1+y2<=1. 0, elsewhere}

For the two chemicals under consideration, an important quantity is the total proportion Y1+Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).

People end up tossing 12% of what they buy at the grocery store. assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. a. calculate the mean and the standard error for the sample proportion p. b. describe the sampling distribution of p in part a. draw a graph of this probability distribution with its mean and standard deviation. what is the probability that your survey will provide a sample proportion more than 15%? c. d. population proportion? what is the probability that your survey will provide a sample proportion within + 0.03 of the