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- 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.)Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :R1
- 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).For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. (d) X = the length of a randomly selected rattlesnake Describe the set of possible values for the variable. 0, 1, 2, 3, ... 1, 2, 3, ... [0, ∞) (0, ∞) State whether the variable is discrete. discrete not discrete (e) Z = the sales tax percentage for a randomly selected amazon.com purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable. z1, z2, z3, ..., zn [0, zn] 1, 2, 3, ..., n [0, n] State whether the variable is discrete. discrete not discrete (f) Y = the pH of a randomly chosen soil sample Describe the set of possible values for the variable. 0, 1, 2, 3, ..., 14 [0, 14] 1, 2, 3, ..., 14 (0, 14] State whether the variable is discrete. discrete not discrete (g) X = the tension (psi) at which a randomly selected…1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.
- Choose points from (0, 1) uniformly and add the numbers together. Stop this process when your add is greater than one. Let N be the random variable which is the number of points that you selected. Find E(N).16) number of medical tests that a patient will have on entering a hospital is a random variable X which can take on the values 0, 1, 2, 3, and 4. If P(X 2)=0.43, find P(X = 3).Three statistically independent random variables X₁, X₂ and X₂ have mean values X₁ =3, X₂ = 6 and X₂ = -2. Find the mean values of the following functions: 1 2 (a) (b) g(X₁, X₂, X3)= X₁ +3X₂ + 4X3 29 g(X₁, X₂, X3) = X₁X₂X₂ 29