tysm po ASAP

1. Identify if the given values are discrete or continuous. a. The number of takers passing the licensure examination per year. b. The amount of sweat an athlete produces after working out. c. The length of time before a computer component fails. d. The number of residential buildings constructed each year in a certain city. e. The average daily temperature in your room. f. The number of days where the time you spend studying in a day is greater than 5 hours. 2. A construction company has 5 dump trucks that they can use for their various projects. Let X denote the number of dump trucks deployed in the field at a specified time. Suppose the pmf of X is as given in the table below. X 0 1 2 3 4 5 f(x) 0.10 0.20 0.25 0.30 0.08 0.07 Calculate the probability of each of the following events: a. { at most two trucks are in use } b. { between two and four trucks, inclusive, are not in use} c. {at least two trucks are in use) d. { fewer than three trucks are in use } 3. Many cement companies have research and development teams that continuously formulate and experiment different composition of chemicals to fully optimize the cement that they produce. Suppose a research team formulates 5 different mixtures every month. Two mixtures are selected at random from each batch for testing. The possible outcomes of the selection process are represented by pairs. For example, the pair (1, 2) represents the selection of mixtures 1 and 2 for testing. a. List all the different possible outcomes of the selection process. b. Suppose that mixtures 4 and 5 do not meet the requirements of the test. Two mixtures are to be chosen at random. Define Y to be the number of mixtures that does not meet the requirements among those tested. Find the probability distribution of Y. c. Find the cumulative distribution function of Y