Let X be a continuous random variable wit cumulative distribution function x < 0 F(x)%= 0sx <3 27 X 2 3
Q: Let X be a continuous random variable witi cumulative distribution function X < 0 F(x)= 0sx <3 27 3
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- What is the likelihood ratio p(x|C₁) p(x|C₂) in the case of Gaussian densities?Let X be a random variable with density function 1) ={0. k(1 -x), if 0<*<1; otherwise. f(x) Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1.Hypergeometric distribution Given user defined numbers k and n, if n cards are drawn from a deck, find the probability that k cards are black. Find the probability that at least k cards are black. INPUT 11 7 OUTPUT 0.1628063397551007 0.24927823677714275
- X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.4. Given a random variable w with den sity F(w) and a random variable p as the umiform im the interval (-71, +71) where wlP (two w and p are independent) R.V.S Suppose the stochastic process, xt) =a Cos (wt+P). meam a) show that xlt) is wss with zero and auto correlation equal R(E) = E (Coswr) j(wt+P) b) show that zt)=aé is also a Wss.Solve In R programmning language: Calculate the probability for each of the following events: (a) A standard normally distributed variable is less than -2.5. (b) A normally distributed variable with mean 35 and standard deviation 6 is larger than 42 but less than 45. (c) A normally distributed variable with mean 35 and standard deviation 6 is larger than 40 but less than 41. (d) X < 0.9 when X has the standard uniform distribution (min=0, max=1). (e) 1 < X < 3 in the exp distribution with rate λ = 2.
- Write a function my_random that samples a random number from the following discrete probability distribution on the set {8, 9, 13, 15, 17, 18}: P({8}) = ²/ 9 P({9}) = ²/ 18 P({13}) = 1/ P({15}) = P({17}) = ²/ 16 NO P({18})= =Let X be a continuous random variable with probability density function = {1/³ fx (x) if -1 < x < 2 otherwise 0 Let Y = X². Find the cumulative distribution function for Y.Using the standard normal distribution, what is the probability that z>1.3936 ? O 0.0409 0.9183 1.8366 0.1634 0.0817
- For a given joint probability distribution f (x, y) where 0 < x < 4 and 0 < y < 5, which of the following equation provides the marginal probability of y? O f f (x, y) dy O S f (x, y) dx S f (x, y) dx O sf f (x, y) dæ2. A discrede random varPable X has the followFny Probability distrbfution: the Value 2. 34 6 7 PO)C 2c 3C c2c4ad 20 d.Let X1, X2, .,X25 be i.i.d. random variables from Po(5). Estimate the MSE for the median estimator using Monte Carlo estimation.