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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?What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
- Derive a general expression for the variance of net future loss Var(L) with a constant force of interest δ under each of the following models:i. μ_x(t) = μii. μ_x(t) = 1/(ω-x)The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
- If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.853. If X has an exponential distribution with λ=2. Calculate the following P(X≤0)=? P(X≥2)=? P(1<X<2)=? The value of x such that P(X<x)=0.05 corresponds to x=?If E(X) = 2 and standard deviation of X is 3, what is E(X2)?