Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the correlation between each pair of different variables is 1/4. Determine Var (X
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Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the
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- Previous Probletn Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5. Find Var(3X-2Y + 3). Please answer to 2 decimal places.Suppose, you are running an experiment for 1024 times where the probability of success in a single experiment is 'p'. If the variance of the number of successful experiments is 256 , find p.2. Let X - tp. Verify the mean and variance formulas. (Hint: Let X = p/2UV-1/2.)
- A nail is needed to hang up a 50 lb painting on a wall. A technician has two nails in his pocket, where the probability that both nails meet the specific weight of the painting is 50%, the probability that only one of them meets the specific weight is 20%, and the probability that neither of them meets the specific weight is 30%. If the number of nails that meet the specification is a random variable, find the variance of the data of that random variable.If X~Gamma(4,6) the the variance of X is 4 24 144 LOLet x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.
- Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the aboveTwo computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 539, the variance of Yis 754, and the covariance of X and Yis 183.50. a) Calculate the correlation coefficient (p) Select one: a. 0.287 b. 0.857 c. None of the answers d. 0.928An arcade machine costs one dollar to play. Every time you play, there is a 1/10 chance of winning.(a) Let A be the number of times you play until you win. Find the variance Var[A].(b) Ten people play the arcade machine; each one keeps playing until they win, and thenit’s the next person’s turn. Let B be the number of times they play in total. Find thevariance Var[B].(c) Ten years later, you come back to the arcade machine, and it’s exactly the same, exceptthat due to inflation, the machine costs $10 to play.Let C be the the total cost of playing until you win. Find the variance Var[C].
- When a random variable X follows binomial distribution, the probability of success on one trian is equal to 0.6, and the number of trials is eual to 120, What is the variance of X ? |------Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater than or equal to 1)A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) These data are shown in the table. Total weight gains (in kg) Ripped Gainz 14.1, 10.9, 12.1, 5.2, 12.0, 17.1, 9.0, 14.8, 11.2, 6.8, 12.4, 8.5, 12.1, 10.5 Send data to calc... v 7.6, 9.5, 8.6, 10.8, 7.9, 10.0, 8.4, 6.2, 8.6, 10.2, 8.9, 8.2 Send data to Excel Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the…
