The probability of an event depends on the random variable X and can be expressed by the following formula: - - e-kx for x ≥ 0, for x < 0 P(A | x) = { 1 (k > 0). Find the total probability of the event A if X is a normally distributed random variable with expectation x and variance o².
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- Calculate the expected value E(X) of the given random variable X. X is the number of tails that come up when a coin is tossed 26 times. E(X) =A kindergarten class consists of 12 boys and 4 girls. The children are arranged from tallest to shortest. Assume that all 16! rankings are equally likely, and no two children are the exactly the same height. let the random variable X be the rank of the second tallest boy. assume that the tallest person in the class is rank 1. (a) find f(x) (b) Calculate E[X] and V[X]The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).
- Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(2The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)Suppose X takes the value 1 with probability P, and the value 0 with probability (1-P). The Probability distribution of X is P(X) 1-P 1 P The expected value of X, E(X) is:Q1A Suppose that the probability of finding defectives within a manufactured lot of electrical fuses is 0.09. Assume the probability distribution function (PDF) is binomial. Let X be the number of defectives within the sample. In a sample of 25 fuses, find the probabilities: (a) P(X 2), (b) P(X > 0), (c) P(1 ≤ X < 4). === B Suppose the discrete random variable X has the PDF as in the table below. Find: (a) F(7), (b) E(4-3X). I 4 6 7 8 9 f(x) 0.2 0.25 0.15 0.3 0.1Let a mixed random variable X have the following distribution. Find expectation of X. Find variance of X.The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(0Let X be the random variable with PMF: p(x) = k(]x – 2|+ 1), for x= -2, -1, 0, 1, 2 0, elsewhere (a) Find the value of k (b)Find the PMF of X (c) Find the mean, variance, and the standard deviation of Xc) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e-²x Determine the expected value of X. } " x ≥ 0The following depression scores are for a sample of ten people who were tested before and after receiving cognitive behavioural therapy. Use Excel and perform the relevant hypothesis test using α = 0.05, following all four key decision-making steps. before after 5 5 6 3 7 5 5 3 8 5 9 7 7 5 5 4 10 9 4 4SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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