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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.The functions i)= e **2f,(x) = e*-3 %3D are O A. Insufficient information to conclude None of them O B. O C. Neither linearly dependent or independent OD. Linearly independent O E. Linearly dependent1. The functions fi(x) = 4x, f2(x) = x² + 6x, and fз(x) = 4x² + 12x do not form a linearly independent set of functions. Verify this by writing one of the given functions as a linear combination of the other two functions. (4 pts.)
- Q7. Thank you!3. Consider this function: g(x) = (x - 273) + 32 . (a) Determine the function which will 'undo' everything this original equation does. All work must be shown! tool.] (b) Describe a way you could "test" your equation in part (a) to see if it truly will 'undo' the original function. [ (c) The original equation is not random! That given equation will convert from a = a known temperature in degrees Kelvin into g(x) =equivalent temperature in degrees Fahrenheit.3.4. Show that if f and g are pdfs and a € [0, 1], then af+(1-a)g is also a pdf.
- Please help me answer (d) and (e).Before a strike prematurely ended the 1994 major league baseball season, Tony Gwynn of the San Diego Padres had 165 hits in 419 at bats, for a .394 batting average. There was discussion about whether Gwynn was a potential .400 hitter that year. This issue can be couched in terms of Gwynn's prob- ability of getting a hit on a particular at bat, call it 0. Let Y; be the Bernoulli(0) indicator equal to unity if Gwynn gets a hit during his ih at bat, and zero otherwise. Then, Y1, Y2, . .., Y, is a random sample from a Bernoulli(0) distribution, where 0 is the probability of success, and n = 419.7. Assume that X is a nonnegative, integer-valued random variable with p.g.f. G(z). Let G(¹) (z) denote the nth derivative of G. Let pk = P{X = k} for k = 0, 1, 2,.... Express each of the following as a function of G. (a) E[X]. (b) E[X(X - 1)]. (c) E[X(X - 1)(x - 2)]. (d) Var(X). (e) po. (f) P1. (g) Pn for n = 0, 1, 2,.... (h) Suppose an archer takes X shots at a target. Assume the shots are inde- pendent, and the archer hits the bullseye on any attempt with probability p. What is the probability that the archer is hits the bullseye on all X attempts? (i) Suppose the effective interest rate per period is i%. What is the present value of one dollar received at time X?
- 16. The resident population P of the District of Columbia (in thousands) from 1995 through 2005 can be modeled by where t is the year, with t = 0 corresponding to 2000. (Source: U.S. Census Bureau) (a) During which year, from 1999 through 2005, was the population the greatest! P = 0.26943 – 2.048/² – 0.73t + 571.9, -12. Let f(x) = 3x(x² − 1) (x³ + 2x + 3) (a) Use distribution to expand the function. (b) Use the rules in from the table above to differentiate the function.
