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Please solve these problems:
1. Suppose that each day there is a 10% chance of rain and whether or not it rains each day is independent of all the other days.
(a) Calculate the probability that we will have to wait at least 5 days for it to rain for the first time (i.e. at least 4 consecutive non-rainy days before the first rain; i.e., it rains no earlier than the 5th day)
(b) Calculate the expected number of non-rainy days before we get the first day that it rains.
2. The number of seahawk nests in the outskirts of Seattle is expected to average about 8.76 per acre. We will suppose that these nests are placed according to a Poisson distribution.
(a) What is the probability that there will be 7 or 8 nests in an acre?
(b) Let Y be the number of nests counted in 15 acres. What is the expected value of Y?
(c) What is the probability that 115 < Y < 120?
MATH1550H: Assignment: Question: A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..
MATH1550H: Assignment: Question: what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?
MATH1550H: Assignment: Question: Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form
MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?
MATH1550H: Assignment: Questions: Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.
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