In a box containing 8 red balls, 8 green balls and 8 blue balls where 3 balls will be drawn in random with replacement, let R be the random variable representing the number of red balls chosen. What is f(0)?
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In a box containing 8 red balls, 8 green balls and 8 blue balls where 3 balls will be drawn in random with replacement, let R be the random variable representing the number of red balls chosen. What is f(0)?
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- The three random variables, a, b and c are independent and each uniformly distributed in the interval (0, 1]. Find the probability that the equation ax? + bx + c = 0 has 2 real roots.Suppose that one variable, x, is chosen randomly and uniformly from [0, 2], and another variable, y, is also chosen randomly and uniformly from [0, 4]. What is the probability that x≤y≤2x+1?The probability for x≤y≤2x+1 isIn a toy shop ,2% of the toys are defective.If a boy selects 4 toys randomly ,find the probabiility of getting atleast one of the toys defective .
- A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests. To test this belief, the teacher recruited 16 students and randomly assigned them to two groups: G1: a group of n1=8 students that studied more than four hours for her test, and G2: a group of n2=8 students that did not study for her test. The following are the data from G1, who studied more than four hours for the test: n1=8 M1=85 s1=5 (this is the standard deviation of the sample, dividing the sum of squares by n1) The following are the data from G2, who did not study for the test: n2=8 M2=75 s2=4 (this is the standard deviation of the sample, dividing the sum of squares by n2) Perform a t-test by answering the questions below. Use an alpha-level of α=.05. 0. Using formulas from Section 4, compute the estimates of the population variances, est. σ12 and est. σ22 (from s1 and s2 above). 1. What is the research…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.)There are 2 players in a game. Each player independently picks a real number on the interval [0, 1] uniformly. If the (absolute) difference between the two numbers is less than a (0 < a < 1) and the sum of the two numbers is less than 1, then both players win, otherwise both players lose. What is the probability of winning? 2.
- It is known that in a certain town 30% of the people own an Kpfone. A researcher asks people at random whether they own an Kpfone. The random variable X represents the number of people asked up to and including the first person who owns an Kpfone. Determine that P(X <6).Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). DetermineNumber 19
- A fair dice with sides numbered with {1, 2, 3, 4, 5, 6} was rolled three times. Let X denote number of times 6 was rolled in the first two rolls and let Y denote the total number of 6 rolled. Find the covariance of X and Y.A researcher selected a sample of 268 former student-athletes from a list of graduates of a large university. A total of 14% of the sample of athletes had earned graduate degrees as compared to 17% of all graduates. What is the Z obtained value?
