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- A fair coin is tossed three times, let's X represent the number of heads that showed up. Determine the probability mass function of x Find the cumulative distribution function The expectation of x The variance of xLet a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?l we LTE 9:33 AM @ 92% Done Edit Let X and Y be independent random variables with X ~ N(0; 1) and Y~ N(0; 2). The value of P(X > Y ) is Select one: a. 0.05 b. 1 C. d. 0.5 More
- Safety switch An industrial machine requires an emer-gency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experi-ment to find out whether workers will be able to deacti-vate the machine as quickly with their left hands as with their right hands. Be sure to explain the role of random-ization in your design.Consider the experiment of tossing a coin twice. (Let H represent the head of the coin and T represent it's tail.) (a) List the experimental outcomes. (Select all that apply.) □ (H) O (T) O (H, H) □ (H, T) □ (T, H) □ (T, T) (b) Define a random variable that represents the number of heads occurring on the two tosses. The random variable x, where x = ---Select--- ✓that occur for ---Select--- (c) Show what value the random variable would assume for each of the experimental outcomes. (If an experimental outcome does not occur, enter NONE.) Outcome Values of x (H) (T) (H, H) (H, T) (T, H) (T, T) ], describes the scenario. (d) Is this random variable discrete or continuous? O continuous O discreteab Jock Determine whether the random variable described is discrete or continuous. The number of defective cell phones in a shipment of 50. # esc K ➜ The random variable described is (Choose one) ▼ Check ! Type here to search 1 ? A @ Z 2 W # * 3 3 X $ S D 4 E R C % LO 5 T 10 6 99+ 4- & Y 7 a F G H V B # 4+ © 2023 McGraw Hill LLC. All Rights R 8 00 J N ( 9 10 11 K M
- 4-10 only4. Instructor's Praise: Suppose the amount of praise an instructor gi ves in his class can be modelled by a Poisson random variable X with rate 3 sentences per class. (a) What is the rate per class (A) and hence the mean and variance of the random variable X. (b) 1,2, 3, 4, 5). (Fill the table below and show all your working) Find the probability that in a particular class he gives I sentences of prai se (where r = (c) that in the next class he gives a sentences of praise (where r= 1,2, 3, 4, 5). Given that the instructor didn't give any praise in the first 10 classes. What is the probability (d) praise, what's the probability that he gave 3 sentences of praise. Find the conditional probability that in a class given that he gives at most 5 sentences of (a) (b) The following are the relevant probabilities: X = r 1 2 3 4 5 P(X = x) (c) The following are the relevant probabilities: | 1 2 3 | 4 |5 X = 1 P(X = x) (d)Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute 2 y. 13 36 23 31 25 26 -13 -13 -23 -2 26 16 24 17 16 -2 -3 -8 92 O 100 O 94 O 102 O 96 co
- Roll a fair die twice let X be the random variable that gives the absolute value of the differences between the two numbers. a)construct the probablityofthe variable X. b) Find the cumulative distribution function(cdf) F(x)What is the probability that Z is equal to or greater than 0.6? Z represents a standard normal continuous random variable. Answer: The probability that Z is greater than b is 55%. What is b? Z represents a standard normal continuous random variable. Answer:topic: function of random variables