i) Calculate the expected value of S. ii) Calculate the variance of S. iii) Determine E (1145 - 7S - 6S²).
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- Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?Assume that ξ has a rectangular distribution with the mean value E(ξ) = 0 and the variance V(ξ) = 12. Calculate P (ξ> 5).Suppose that f (x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.
- Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i=1,..., n.With unit variance; the random variable Y is related to the random variable X by a linear relationship. A. Calculate the minimum error power when X and Y are fully correlated. B. Calculate the minimum error power when X and Y are not related at all.Toss a coin three times. Let H₁ be the event of getting a head and T¡ of getting a tail at ith time for i=1,2,3. Which of the following events is the event of getting at least one head in the three tosses. T₂ T3 T₁ O H₁ H₂ H3 T₁ U T₂ U T3 H₁ U H₂ U H3 O H₁ U H₂ H3 Submit Answer Tries 0/3 The complement of getting at least one head is Getting all the tails Getting at least one tail Н1 П Н2 П Н3 T₁ U T₂ U T3 Getting all the heads Submit Answer Tries 0/3 Answer True or False to the following statements ✓ H₁ and H₂ are mutually exclusive H₁ and T₂ are mutually exclusive |T₁ U T₂ and T3 are not mutually exclusive T₁ and H₂ are mutually exclusive ✓ T1₁ and H₂ are mutually exclusive Submit Answer Tries 0/3 A and B are two events. Answer True or False to the following statements (There could be more than 1 correct statements) ✓A is a subset of AB ✓A is a subset of A U B ✓AB is a subset of A U B AUB is a subset of AB A B is a subset of A
- If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? ExplainThe probability mass function of a discrete random variable Y is given by k y = 2, 3,4, 5 p(y) = { 6- y 0, PV) : elsewhereLet X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows. 2 3 4 P(x) 0.1 0.2 0.1 0.2 0.4 Send data to Excel
- Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the probabilityP(6.3x )=0.36.The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X is var(X) =4. Using the equation Y = 11X + 81. What are the expected value E(Y), variance VAR(Y), and standard deviation SD(Y) of this expression.