(8) X and Y are independent events. P(X)=0.3; P(Y)=0.4. Find (d) P(X or Y) (9) Repeat the previous problem if X and Y are mutually exclusive
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(8) X and Y are independent
(d) P(X or Y)
(9) Repeat the previous problem if X and Y are mutually exclusive.
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- 3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?J 2 10. Airlines routinely overbook flights to help lower the number of empty seats on their airplanes in order to increase profits. In the year 2005, the no-show rate was estimated to be 12%, with 88% of passengers with tickets actually showing up to take the flight. Suppose an airplane has 25 seats, and that the airline has sold 27 tickets. What is the probability that there will not be enough seats? 11. Referring to the no-show rates from Problem 10, out of 27 tickets sold, what are the mean and standard deviation for the number of people that show up to take the flight need answer for 11!If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).
- Q)There are two tests for a disease, one is rapid and the other is slow. Given that an individual is infected, the rapid test will register positive 40% of the time, while the slow test will register positive 80% of the time; additionally, both tests will be positive 35% of the time. Assume currently, 20% of the population has the virus. Use Bayes theorem to calculate the chance that a person has the virus conditioned on getting negative results for both tests?If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine E(x),var(2x) and pr(X>1)
- Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)A hypothesis test produces a t statistic of t = +2.19. If the researcher is conducting a two-tailed hypothesis test with α = .05, how large does the sample have to be in order to reject the null hypothesis?You are considering purchasing stand-alone shares in two companies: Company A and Company B. While both companies expect a rate of return of 15% under normal market conditions, the possible returns under strong and weak economies differ. There is a 30% chance of a weak economy outcome, a 30% chance of a strong economy outcome, and a 40% chance of a normal outcome. For Company A, under a strong economy, they expect a return of 75%. Under a weak economy, they expect a return of -45%. For Company B, under a strong economy, they expect a return of 23%. Under a weak economy, they expect a return of 7.5%. 1. Create a probability distribution table for both companies. 2. Calculate the standard deviation for both companies. 3. With the distribution, create either a bar graph or a bell curve to graph the two companies. 4. From your calculations, describe which company you would consider investing in, if you were risk averse.
- (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.(X³, 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given random variables.If two events are statistically independent, then the probability that they both occur is: a. 0 b. 0.5 c. 1.0 d. the product of their marginal probabilities e. cannot be determined with the information given.