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- Suppose that the joint probability for random variables X and Y defined by 29 28 3. 28 28 The mean of the random variable Y. HY.is 39 28 27 28 41 28Let X - binomial (n, p) and Y ~ binomial (m, p) be independent. a. Derive the MGF of W = X+Y. b. By the uniqueness property of the MGF, what is the probability distribution of W? c. Find the mean and variance of W using its MGF.2. Let X be the mean of a random sample of n = 25 from N(30, 9). Find the probability that the sample mean is between 29.8 and 30.6.
- Exercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?Q2. If the lifetime X of a hearing aid battery has Weibull distribution with a = 0.1,B = 0.5. Find the probability that such a battery a) Find varince2. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTM
- Determine if the random variables X and Y are statistically INDEPENDENT or not; show solution.pls answer completely.Let X and Y be 2 random variables with joint probability distribution given in the following table: f(x,y) 1 3 0.3 0.2 Y 4 0.1 0.4 Then f(Y = 3|X = 0) is equal to: a. 0 b. 0.5 c. 0.75 d. 1