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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Let X1, X2, ..., X, be independent random variables and Y = min{X1, X2, ..., Xm}. Fy (y) = 1 – || (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are independent, find the mean and variance of Y = X1 – 2X2+3X3.
- by the formula The expectation of the number of defective devices is given - N[₁ - (1 - 2N)"]· ΩΝ T = where P is the probability that the trial of one device is considered successful, is the average number of successful trials until the first failure occurs, N is the number of devices tested and m is the number of trials (successes and failures) for each device. Using the linearization method, find the dependence of the expectation and variance of the random variable T on m if N, P and 2 are independent random variables, whose expectations and variances are: M[N] = 5, M[P] = 0.8, Μ[Ω] = 4, D[N] = 1, D[P] = 0.1, D[P] = 0.2.A scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2 through the equation y = ae+Px2 8, where & is a random error that is always positive. Find a transformation of the data that will enable her to use a linear model to estimate B, and B,.Let u(X) be a nonnegative function of a random variable X. It can be shown that P(u(X) >= c) <= E(u(X)) / c Suppose X is a random variable with momonet generating function Mx(t). Show that P(X>= a) <= exp(-ta) * Mx(t) Thank you
- Let X1, X2, X3 be random variables each having a mean u and variance o. Further, Cov(X1, X2) = 2, Cov(X1.X3) = 3 and Cov(X2, X3) = 1 Define U = 2X1 – X2 + 4 X3 Solve for the mean and standard deviation of U.2. You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: Studentl= 71.0– 4.84×BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) a. What is the interpretation of the intercept? What is the interpretation of the slope? How tall are females, on average? b. Test the hypothesis that females, on average, are shorter than males, at the 1% level. c. Is it likely that the error term is homoskedastic here?Let X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might not be independent.) What is the maximum possible value of Var(3X − 2Y + 4)?
