Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either...

Extracted text: Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and finds the following distribution of traits: open closed 3 leaves N3,0pen N3,closed 5 leaves N5,0pen N5,closed a) Assuming the two traits are independent, determine the expectations of the counts N3.open; N3,closed, N5,open, in the table. and N5,closed b) Determine an approximate value for the probability P(N3,0open > 340).