Consider two random variables X and Y with p(X, Y) = 0. Which of the following statements is always correct? O a. X and Y are independent but correlated. O b. X and Y are uncorrelated. O c. X and Y are independent. O d. X and Y are uncorrelated but not independent.
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- Consider the following random experiment: we toss a two-sided coin (H on one side and T on the other side) n = 3616 times. In any given toss, the probability the coin comes up H is p = P(H) = 0.3. Each time the coin comes up H we give Tom 2 dollars and each time the coin comes up T we take from Tom 1 dollar (so Tom either gets 2 or gets -1, i.e., loses 1 dollar). How many dollars do we expect Tom will get on "average", i.e., per experiment?Suppose the probability of having blood type A is 0.10. Let X be the number of people with type A in the experiment of selecting one thousand random people. 1. The values of the random variable X is x = _____. A. {1, 2, …} B. {0, 1, 2, …} C. {1, 2, …, 1000} D. {0, 1, 2, …, 1000} 2. Which of the following is(are) correct? Then, explain whyI. The probability of each value of x is between 0 & 1II. The probability that one thousand people will have blood type B is 1 A. I onlyB. II onlyC. Both I and IID. Neither I nor IIDetermine the value/s of the random variable in each of the following situations: A box contains three colors of marbles - white, black, and yellow. Three balls are picked one at a time with replacement. Let U be the number of yellow marbles that appear. A. 3 B. 1 C. 0 D. 0, 1, 2, 3 E. 0, 1, 2 F. 0, 1 G. 2
- Let N be the last digit of your student number. Let X and Y be two continuous random variables that have the correlation coefficient c=0.1(N+1). Which of the following statements are true? (Wrongly ticked answers will reduce your marks in this question) a. X and Y are positively correlated. b. O c. X and Y are statistically independent. The sum of E[X] and E[Y] is equal to E[X+Y]. Od. X and Y are negatively correlated. e. The sum of Var(X) and Var(Y) is equal to Var (X+Y).a?If a variable can take certain integer values between two given points, then it is called O a. Continuous random variable O b. Probabilistic random variable c. O c. Deterministic random variable O d. Uncertain random variable O e. Discrete random variable
- 17. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choicesAssume the following data displays the joint probability for random variables X and Y: X 10 20 30 20 0.1 0.2 0.05 0.05 0.1 0.2 0.2 0.0 0.1 -1 Y O 1 1. Solve for the correlation of X and Y. 2. Solve for the correlation of X and Y conditional on Y being greater than or equal to zero. 3. Are X and Y independent? Are X and Y conditional on Y being greater than or equal to zero, independent.○ Let assume 6 balls, 3 white, 2 black and 1 red. Random experiment is selection of three balls with replacement. R.v. X denoted number of white balls and r.v. Y denotes number of red balls. O P(X=2, Y-2)= 0 O Probability of which events is zero? O P(X=1, Y=2) = Compute joint pmf of X and Y
- Q1. The table below shows voters choose at random between African American and African American democrats: Republican Democrats Total African-American 4 12 16 White/others 44 40 84 Total 48 52 100 Using the above table find the probability that the voter is either African American or Democrathand write asapIn a random experiment if a coin is tossed three times or three coins are tossed one time, if random variable X is the number of appearances of Tails, the value of E(X), will be; Select one: O a. None O b. 3.5 O c. 2.5 O d. 1.5