In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas.)
1. Suppose we have a computer program that attempts to answer a yes or no question for us. The probability that the program will return the correct response 0.6. Suppose we run the program 15 times. Let X be the total number of times that the program returns the correct answer.
a. What kind of random variable is X? What is the pmf?
b. What is the mean and standard deviation?
c. What is the probability that the computer returns the right answer exactly 3 times? Less than 3 times? More than 7 times?
d. What is the probability that the computer returns the right answer less often than the wrong answer?
In each problem, make sure that you are clearly defining random variables, stating their distributions, and...
In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas.) Prove that the exponential distribution is memoryless. That is, let X~Exp(?), and show that for any two positive real numbers x, y, P(X ≥ x + y | X ≥ y) = P(X ≥ x). Hint: Mirror the proof we did in class for...
In each problem, make sure that you are clearly defining random variables, stating their distributions, and writing down the formulas that you are using. (That is, write down the pmf, write down mean and variance formulas. 6. John has been talking some mad smack about Fred, claiming to be leagues better than Fred at rock-paper-scissors. Suppose that despite talking some smack, John is just plain whack, and Fred is the better player, with a probability of 0.6 of winning any...
Suppose we have a computer program that attempts to answer a yes or no question for us. The probability that the program will return the correct response 0.6. Suppose we run the program 15 times. Let X be the total number of times that the program returns the correct answer. What kind of random variable is X? What is the pmf? What is the mean and standard deviation? What is the probability that the computer returns the right answer exactly...
O RANDOM VARIABLES AND DISTRIBUTIONS Binomial problems: Advanced A multiple-choice test consists of 8 questions. Each question has answer choices of a, b, c, d, and e, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets fewer than 3 of them correct? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal nlaces (If necessary, consult a list of...
O RANDOM VARIABLES AND DISTRIBUTIONS Standard normal values: Advanced Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(0.6<Z<c)-0.2573 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. 1× 5 ? Explanation Check PROBABILITY The curious die A peculiar die has the following properties: on any roll the probability of rolling either a 2, a 5, or a lis just...
Please answer from a-d Problem 2. Let X be a random variable with one of the following cumulative distribution function. 1.2 1,2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2,0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 X X Pick the correct cumulative distribution function plot and answer questions: Page 2 of 9 Write down the probability mass function and What is the PMF of X? A. Poisson (3...
Sampling Distributions 1. An automatic machine used to ill cans of soup has a mean flling weight of 16 ounces and a standard deviation of 0.5 ounces. a. What is probability of obtaining a sample of 49 cans with a mean larger than 16.1 b. Find the probability that the sample mean will be within 005 ounces of the population ounces? mean, 16 ounces. 2. Family income distribution in St. Paul, Minnesota, is skewed to the right. The latest census...
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6), i.e., the probability that the first value collected is less than 2.6. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 3? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum...
please write clearly thank you very much 6. (20 pts) A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent duathlon deviation of 0.25 hours. Suppose a random sample of 30 participants finishing ti was 1.67 hours with a standard was taken and the mean me was found to be 1.59 hours with a standard deviation of 0.30 hours. (a)...
Writing the code in IDLE. Make sure the code is working. thank you so much Create the following turtle pattern. Using the turtle and random modules, write a program that creates an output as the one shown in the picture below. Consider the following: . Change the color of the window to "red" using wn.bgcolor property of the screen variable you create. . Your turtle variable has to have a pen color "white", you have to use the .pencolor property...