12. Suppose the pdf is given by f(x)Cx2 for 1 < I < 2, and zerootherwise.(a) Find the value of C.(b) Find the likelihood that a point selected at random with respectto this pdf is between 1.5 and 2(c) With X(x) = x, find E(X) and Var(X)

The total probability under a probability density curve is 1. Integrating f(x) from 1 to 2 and…

Answered: 12. Suppose the pdf is given by f(x)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.
Please help me answer (d) and (e).
2.8.59 Let f(x)= 4x-1, h(x)=-x+4. Find (fo h)(-2). (foh)(-2) =
(d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.
5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Streated (survival probability of patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined to be: Streated(t) = e-(15)" and Splacebo (t) = e 15t 144. (a) "Ise the given function 15t Ppiacevo \" e-144 to calculate %3D Spreated the average survival probability of the placebo group for the first 10 months of the study. Round to 2 decimal places. 5-0:8 -0:6 Splacebo -0:4 0:2 10 20 (b) The efficacy of the drug at any timer > 0 can be defined as E(T) = | (Streated(t) – Splacebo (t)) dt. Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Round your final answer to 2 decimal places. (c) the first T months). Is the drug beneficial at…
5. Suppose the study conducted showing gender difference in salary of management graduates students Y=25.20 +8.25D + 1.25X t (32.85) (10.45) (15.11) Where Y is income in thousands Find, D is a dummy variable taking on the value of 1 if male 0 for female X = years of experience a. Mean salary of females assuming zero years of experience b. Mean salary of Males assuming three years of experience
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Exercise 1. A polling firm determines that the percent of likely voters who support a certain mayoral candidate can be represented by a function P(t) where t is measured in weeks since the candidate entered the race. Suppose P(7) = 15. What does P'(7) = 4 mean? (a) B. (b) If P'(7) = 4, what percent of likely voters do we expect to support this candidate 8 weeks after she entered the race?
5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Streated (survival probability of patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined to be: Streated(t) = e-() and Splacebo (t) = e #. Use the given function (a) Splacebo (t) = e-i to calculate the average survival probability of the placebo group for the first 10 months of the study. Round to 2 decimal places. Ste 0. -0.6 -0:4 -02 10 20 (b) The efficacy of the drug at any time 7 >0 can be defined as E(7) = (Streated(t) – Splacebo (t)) dt. Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Round your final answer to 2 decimal places. (c) the first 7 months). Is the drug beneficial at 10 months? (A short one-sentence…
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period o heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x! f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x) = x< 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to three decimal places.) 016 Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to three decimal places.) .014 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your answers to three decimal places.) mean .6 standard deviation (e) What is the probability that headway is within 1…
(13) Let X b(6,-) find E(5+6x) and distribution function. 3

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12. Suppose the pdf is given by f(x) Cx2 for 1 < I < 2, and zero otherwise. (a) Find the value of C. (b) Find the likelihood that a point selected at random with respect to this pdf is between 1.5 and 2 (c) With X(x) = x, find E(X) and Var(X)