Question 2: Discrete random variables (35 points) Let X = the number of vaccines given per day. The probability mass fun

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Question 2 Discrete Random Variables 35 Points Let X The Number Of Vaccines Given Per Day The Probability Mass Fun 1 (115.07 KiB) Viewed 112 times

Question 2: Discrete random variables (35 points) Let X = the number of vaccines given per day. The probability mass function is given in the table below. x p(x) 0 0.1 5 0.2 10 ? 15 0.3 a) What is the probability that 10 people will get the vaccine? Explain your answer in detail. [10 points) b) Plot the probability mass function of X. (5 points) c) What is the probability that between 2 and 15 people inclusive will get the vaccine? [10 points) d) What is the probability that the number of people that will get the vaccine is strictly between 0 and 10? [10 points)

Question 3: Discrete random variables (30 Points) Suppose that at a certain university, 95% of all students pass the final exam. Four students are to be selected at random; let X denote the number among the four who passed the final exam. a) How many possible outcomes are there for this random experiment? Show the steps of your calculations. [5 points) b) List all possible outcomes for this random experiment. [5 points) c) Find the probability distribution of X. [10 points) d) What is the most likely value for X? [5 points) e) What is the probability that at least two of the four selected students pass the final exam? [5 points)