Table 1 shows the probabilty distribution of the number of wing beats per second for a species of large moth while it is flying. Let X denote the number of wing beats per second for the large moth species while it is flying.1 a) What is the probability that the number of wing beats per second of a randomly selected large moth will be 8? (b) What is the probability that the number of wing beats per second of a randomly selected large moth will be no more than 7? (c) What is the probability that the number of wing beats per second of a randomly selected large moth will be at least 8? (d) What is the probability that the number of wing beats per second of a randomly selected large moth is between 6 and 9 (both inclusive)? (e) What is the expected number of wing beats per second of a randomly selected large moth? f) Find the variance of X and the standard deviation of X. 2. In a certain population of mussels (Mytilus edulis), 80% of the mussels are infected with an intestinal parasite. Suppose 25 mussels are randomly chosen from the population. Let X denote the number of mussels in the sample of 25 mussels that are infected with an intestinal parasite. Use Table I of the statistical tables sheet to find the probabilities in the following questions.2 (a) What is the distribution of X? (b) How many mussels infected with an intestinal parasite do we expect to observe in the sample? (c) What is the variance of X? (d) What is the probability that at least 21 mussels in the sample are infected with an intestinal parasite? (e) What is the probability that 18 mussels in the sample are infected with an intestinal parasite? (f) What is the probability that between 20 and 23 (both inclusive) mussels in the sample are infected with an intestinal parasite? (g) Write down the R command in the space provided below to calculate the probability in part (e). > (h) Write down the R commands in the space provided below to calculate the probability in part (f). > > > k1 <− > 3. Let S = {E1, E2} be the sample space of an experiment where E1 and E2 are the simple events in S. What is P(E1) if E2 is three times more likely to occur than E1? (a) 0.65 (b) 0.33 (c) 0.20 (d) 0.25 4. Consider the events A and B in an experiment where P(A) = 0.35, P(B) = 0.40 and P(A ∩ B) = 0.30. What is P(A ∩ B0 )? (a) 0.65 (b) 0.05 (c) 0.55 (d) 0.80 5. Consider the events A and B in an experiment where P(A) = 0.35, P(B) = 0.40 and P(A ∩ B) = 0.30. What is P(A ∪ B0 )? (a) 0.90 (b) 0.70 (c) 0.55 (d) 0.30 6. Consider the events A and B in an experiment where P(A) = 0.35, P(B) = 0.40 and P(A ∩ B) = 0.30. What is P(A0 |B)? (a) 0.90 (b) 0.55 (c) 0.25 (d) 0.75 7. Circle the incorrect statement below. (a) The sum of the probabilities of all simple events in the sample space is equal to 1. (b) The probability of an event A is equal to the sum of all simple events in A. (c) The probability of an empty set is equal to 0. (d) The probability of a simple event must lie between 0 and 1.