Problem 2....
Let X a normal random variable with mean / and variance of . Consider Z = X - H Then Z isa O normal random variable standard normal random variable O geometric random variable O uniform continuous random variable O Bernoulli random variable O Binomial random variable O exponential random variableDetermine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The time it takes to fly from City A to City B C. The response to the survey question "Did you smoke in the last week?" d. The number of statistics students now reading a book e. The amount of rain in City B during April f. The weight of a T-bone steak O C. It is not a random variable. d. Is the number of statistics students now reading a book a discrete random variable, a 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. 0. Is the amount of rain in City B during April a discrete random variable, a 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. f. Is the weight of a T-bone steak a discrete random variable, a 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.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 variableProblem 2: Consider the following discrete bivariate distribution: (0.5(x+y) = = 1,2,... Px,Y(x, y) = y = 1, 2, ... otherwise . Calculate the probability of the event P(X - Y = 2). . Calculate the marginal PMF of X
