An oocyte is a female germ cell involved in reproduction. Based on analyses of a large sample, the article "Reproductive Traits of Pioneer Gastropod Species Colonizing DeepSea Hydrothermal Vents After an Eruption" (Marine Biology, 2011: 181-192) proposed the following mixture of normal distributions as a model for the distribution of X 5 oocyte diameter (mm):
here f1 and f2 are normal pdfs. Suggested parameter
a. What is the expected (i.e. mean) value of oocyte diameter?
b. What is the probability that oocyte diameter is between 4.4 mm and 5.0 mm? [Hint: Write an expression for the corresponding integral, carry the integral operation through to the two components, and then use the fact that each component is a
c. What is the probability that oocyte diameter is smaller than its mean value? What does this imply about the shape of the density curve?