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- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?Let f(x) = kx2(5 – x) if 0 5. (a) For what value of k is fa probability density function? k %3D (b) For that value of k, find P(x 2 3). (c) For that value of k, find the mean.If X has the exponential distribution given by f(x) =0.5 e−0.5x, x > 0, find the probability that x > 1.
- Which of the following is a valid pdf (accounting for rounding)? a.) f(x)= (x2+2)/10 x= 1,2 b.) f(x)= (x2-2)/7 x= 1,2,3 c.) f(x)= 3(x3/x) x= 0.2, 0.3655, 0.4 d.) f(x)= (x+1)/3 e.) x/50 x= 10, 20, 30Statement Q1. The lifetime, in years, of a certain type of fuel cell is a random variable with probability density function x>0 S(x) ={(x+3) Using Determine the value k so that f(x) becomes a pdf. Using cumulative distribution function (CDF) method finds the probability that a fuel cell lasts more than 5 years? Find the coefficient of variation of x+3 P(X>20|X<40). i. ii. ii. iv. Q 2. (a) The probability that a student passes the P&S exam is 0.7. (i)Find the probability that a given student will pass the P&S exam after the third try. (ii)Find the probability that the third student who fails the P&S exam is found after the fifth student in a class of 9 students? (iii)Find the probability that at most 3 students will pass the P&S exam in a class of 7 students. (h) A aomni har muar hra un ir timar par month find. Consider this pdf: f(X) = -X (1Statement Q1. The lifetime, in years, of a certain type of fuel cell is a random variable with probability density function x>0 S(x) ={ (x+3)* Using i. Determine the value k so that f(x) becomes a pdf. Using cumulative distribution function (CDF) method finds the probability that a fuel cell lasts more than 5 years? Find the coefficient of variation of x+3 P(X>20 | X<40). ii. iii. iv.[2] X is an exponential random variable with variance 9. If (X, Y = (2, otherwise, 1(22) Let X = b(6, find E(5+6x) and distribution function.If X has a exponential distribution with parameter 2,find the p.d.f of Y=log X.The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…TF.12 The joint pdf of the lifetimes X and Y in years of two batteries working in parallel is (see picture) a) Find the probability P(Y ≤ 0.5). b) Find the expected values E(X) and E(XY).SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage