1.Dengue-fever viruses are carried by mosquitoes. There are several different serotypes of the dengue virus, and one study showed that, of all mosquitoes that carried serotype (A) , a proportion of 0.31 also carried serotype (B). If the proportion of serotypes (A) and (B) in the mosquito population are 0.1 and 0.8, respectively, what is the probability that a randomly selected mosquito carrying serotype (B) also carries serotype (A)? Round your answer to five decimal places.

2.A probability density function for the random variable X is given by =, where k is a constant. What value must k be if X takes on integer values between 0 and 43? Round your answer to five decimal places.

3.Given the following PDF

i 2 44.2 98 12.5 25

p_i 0.16 0.09 0.1 0.15 0.5 what is E[X]?

4. Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are limited by how effectively parents can incubate their eggs. Suppose that on average, gulls have a 20.2% of laying 1 egg, 30.5% of laying 2 eggs, 18.9% chance of laying 3 eggs, and 30.4% chance of laying 4 eggs. What is the expected value of the number of eggs laid by a random sample of 100 gulls? Round your answer to five decimal places.