In a psychology experiment, the time t, in seconds, that it takes a rat to learn its way through a maze is an exponentially distributed random variable with the probability density function f(t) = 0.03 e -0.03t, o st
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- Need solution of a part. Asap. I will appreciate your Answer.Consider two independent random variables, S and T, which are both exponentially distributed with the same rate λ. Determine the probability density functions ofthe following random variable: R = S + T.Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential distribution with an unknown parameter 0 > 0. The probability density function of this distribution is given by f(x; 0) = 0e 0¹, x > 0. The four most recent intervals between eruptions (in minutes) are x₁ = 32, x₂ = 10, x3 = 28, x4 = 60; their values are to be treated as a random sample from the exponential distribution. (a) Show that the likelihood of based on these data is given by L(0) 04-1306 = (b) Show that L'(0) is of the form L'(0) = 0³ e 1300 (4- 1300). (c) Show that the maximum likelihood estimate of 0 based on the data is ~ 0.0308 making your argument clear. (d) Explain in detail how the maximum likelihood estimate of that you have just obtained in part (c) relates to the maximum likelihood estimator of for an exponential distribution.
- Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by f(y) = -10 ye 10 100 0For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1Let theta be the unknown market share that a company has for its primary product. Uncertainty in theta is represented by a probability density function of the beta distributional form with a = 54 and b = 46. You have developed the posterior distribution for theta after observing that 64 out of a random sample of 90 customers used the product. Which statement is correct? O A. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, but this discrepancy has not affected the mean of the posterior distribution. B. In the sample, the proportion of people who used the product is less than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but greater then the sample mean. O C. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean…For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <The time a randomly selected student spends completing a one-hour test is a random variable with probability density. - {3* 0 < x <1 f(x) = { 2 + x ellers. Find the probability that the student will finish in less than half an hour.For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [5,9] 28 a) Find the mean. %3D (Round to three decimal places as needed.) b) Find the standard deviation. (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)The probability mass function of the r.v.x is 1 -2 0.15 f(x) = P(X=x) 0.45 0.3 0.10 The standard deviation of x is O A. 1.608 O B. 2.006 OC. 1.469 O D. 1.430Below is the life table of a population of waterbuck. What is the probability that an individual in stage 2 will survive to stage 3 (give your answer to three decimal places)? Stage 0 1 2 3 4 5 ax 50 39 25 20 11 4 Answer: 0.200 1.00 0.78 0.50 0.40 0.22 0.08 Ix dx 11 14 5 9 7 4 Probability of survival = lx+1/lx The correct answer is: 0.8 0.220 0.359 0.200 0.450 0.636 1.000 qx XSEE MORE QUESTIONSRecommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning