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- A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If X is the number of defective sets purchased by the hotel, (a) find the probability distribution of X, express it in a table format. Probability distribution of X X P(X) (b) Find the cdf of X. (c) Find the E(X) and Var(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).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:
- Let X denotes the number of patients who die at a certain hospital in a day. The following table gives the probability function of X. 1 3 4. P(X= x) 0.3 0.25 0.25 0.15 0.05 Find the P(1< X <4) O 0.4 0.95 0.7 O 0.5Q1A 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 0.1For any number of x, the cumulative distribution function (F(x)) is the probability that the observed value of the X will be at most x. Select one: True False
- Which of the following is not a property of a discrete probability distribution being valid? All values of P(x) must be positive. All values of P(x) must fall between 0 and 1. All values of x must be positive. The sum of all P(x) values must be 1.The following table is a partial probability distribution for the MRA Company's projected profits (x = profit in $1,000s) for the first year of operation (the negative value denotes a loss). x f(x) −100 0.100 0.2050 0.30100 0.25150 0.10200 (a) What is the proper value for f(200)? f(200) = What is your interpretation of this value? This is the ---Select--- percent probability that the MRA will have a $200,000 profit. (b) What is the probability that MRA will be profitable? (c) What is the probability that MRA will make at least $100,000? Please only correct and with concept and dont do handwritten or skip please!!The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115
