Calculate the expected value E(X) for the given random variable X. Select 13 cards without replacement from a standard deck of 52, and let X be the number of red cards you draw. E(X) =
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- A student takes a test in which they have to indicate whether each of n statements is true or false. The student knows nothing at all about the subject matter and guesses the answers randomly. Let X denote the number of correct answers (a) Write down expressions for the expectation, E(X), and the variance, var(X). Suppose the student gets three marks for every correct answer but loses one mark for every incorrect answer. Let Y denote the student’s total score. (b) Show that Y = 4X −n. (c) Write down expressions for E(Y ) and var(Y ).Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of light bulbs that burn out in the next week in a room with 20 bulbs. (b) The weight of a T-bone steak. ... (a) Is the number of light bulbs that burn out in the next week in a room with 20 bulbs discrete or continuous? OA. The random variable is continuous. The possible values are x = 0, 1, 2,..., 20. OB. The random variable is continuous. The possible values are 0≤x≤20. OC. The random variable is discrete. The possible values are x = 0, = 0, 1, 2,..., 20. O D. The random variable is discrete. The possible values are 0≤x≤20. (b) Is the weight of a T-bone steak discrete or continuous? O A. The random variable is discrete. The possible values are w= 1, 2, 3, .... OB. The random variable is continuous. The possible values are w=1, 2, 3, .... OC. The random variable is discrete. The possible values are w> 0. OD. The random variable is continuous.…Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. x P(x) 0 0.033 1 0.161 2 0.306 3 0.306 4 0.161 5 0.033 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, not every probability is between 0 and 1 inclusive. C. No, the sum of all the probabilities is not equal to 1. D. No, the random variable x's number values are not associated with probabilities. E. No, the random variable x is…
- Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 67 64 75 86 73 73 y 44 39 48 51 44 51 (d) Find the predicted percentage of successful field goals for a player with x = 81% successful free throws. (Round your answer to two decimal places.) %(e) Find a 90% confidence interval for y when x = 81. (Round your answers to one decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.) t critical t (g) Find a 90% confidence interval for β. (Round your answers to three decimal places.) lower limit upper limitFill in the P (X = x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are −3, 2, 4, 5, and 6. Value x of X P (X = x) −3 2 0.11 4 0.20 5 6 0.16Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 21 0 12 11 31 21 11 −14 −17 −8 y: 8 −2 26 14 15 21 13 −2 −2 −2 (a) Compute Σx, Σx2, Σy, Σy2. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to four decimal places.) x y x s2 s (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) x y Lower Limit Upper Limit
- Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. X P(x) 0 0.033 1 0.162 0.305 0.305 0.162 0.033 2 3 O A. G= child(ren) (Round to one decimal place as needed.) O B. The table does not show a probability distribution. 4 5 A. Yes, the table shows a probability distribution. B. No, the sum of all the probabilities is not equal to 1. C. No, the random variable x's number values are not associated with probabilities. D. No, not every probability is between 0 and 1 inclusive. ☐E. No, the random variable x is categorical instead of numerical. Find the mean of the random variable…Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $1000, 3 prizes of $200, 5 prizes of $20, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket Let X be the random variable for the amount won on a single raffle ticket. E(X)= dollars
- Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. P(x) 0.032 1 0.161 2 0.307 3 0.307 4 0.161 5 0.032 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable x is categorical instead of numerical. C. No, the random variable x's number values are not associated with probabilities. D. No, not every probability is between 0 and 1 inclusive. E. No, the sum of all the probabilities is not equal to 1.Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood.t Let x be a random variable representing percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n = 12 blood tests given to a heavy smoker gave the following results (percent carboxyhemoglobin in the blood). Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. 9.1 9.8 10.4 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 (a) Use your calculator to calculate x and s. (Round your answers to four decimal places.) X = S = (b) A long-term population mean u = 10% is considered a health risk. However, a long-term population mean above 10% is considered a…it is multichoice, thank you!
