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Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable, a. The height of a randomly selected person b. The "yes" or "no" response to a survey question c. The number of pigeons in a country d. The number of statistics students now doing their homework e. The distance a football travels in the air after being thrown f. The exact time it takes to evaluate 67 + 29 a. Is the height of a randomly selected person a discrete random variable, continuous random variable, or not a random variable? O A. It is a continuous random variable B. It is a discrete random variable. O C. It is not a random variable b. Is the "yes" or "no" response to a survey question a discrete random variable, continuous random variable, or not a random variable? O A. It is a continuous random variable O B. It is a discrete random variable. O C. It is not a random variable. C. Is the number of pigeons in a country a discrete random variable, continuous randorn variable, or not a random variable? O A. It is a continuous random variable. O B. It is a discrete random variable O C. It is not a random variable. d. Is the number of statistics students now doing their homework a discrete random variable, continuous random variable, or not a random variable? O A. It is a continuous random variable O B. It is a discrete random variable, O C. It is not a random variable. @. Is the distance a football travels in the air after being thrown a discrete random variable, continuous random variable, or not a random variable ? O A. It is a discrete random variable O B. It is a continuous random variableDetermine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The square footage of a pool b. The last book a person in City A read c. The number of people in a restaurant that has a capacity of 200 d. The number of hits to a website in a week e. The height of a randomly selected person f. The amount of rain in City A during July a. Is the square footage of a pool a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. b. Is the last book a person in City A read a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. c. Is the number of people in a restaurant that has a capacity of 200 a discrete random variable, continuous random variable, or not a random variable? O A. It is a continuous random variable. O B. It is a discrete random variable. O C. It is not a random variable. d. Is the number of hits to a website in a week a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. e. Is the height of a randomly selected person a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable.2, Consider X is a bivariate normal distribution N(p,)) with u' = (1,3) and 2 E = : 2 a. Write out the bivariate normal density of X. b. Determine the distribution X1 + 2 X2 c. Determine principal components Y1 and Y2, and calculate proportions of total variance explained by Y1 and Y2. d. Determine and accurately sketch the constant density contours that contain 50% (90%) of probability of the distribution X.Problem 2: 2.1) Write down the mathematical definition of each of the following. (Be precise in your definitions. Each definition should be a mathematical statement.) (a) A random variable (b) The pdf of a random variable. (Specify whether the random variable is discrete or continuous.) (c) The pmf of a random variable. (Specify whether the random variable is discrete or continuous.) (d) The cdf of a random variable. (Specify whether there are any restrictions on whether the random variable is discrete or continuous.) (e) the expected value of a random variable. (Give separate expressions for discrete and continuous random variables.) (f) the expected value of a function of a random variable. (Give separate expressions for discrete and continuous random variables.) 2.2) Write down the mathematical definition of each of the following random variables. (Each definition should be a mathematical statement.) For any parameters of the distribution, explain the meaning of each parameter. Specify whether each of these is a discrete or continuous random variable. (a) a Bernoulli random variable (b) a Binomial random variable (c) a geometric random variable (d) a Poisson random variable (e) a uniform random variable (f) an exponential random variable (g) a normal (or Gaussian) random variable