4.11 For the ARMA(1,2) model Y₁ = 0.8Y₁ _ 1 + e + 0.7et-1 +0.6et -– 2, show that (a) Pk = 0.8pk-1 for k > 2. (b) p₂ = 0.8p₁ +0.60² /10.

Compute Au, where A Au = = 1 (56) 4 and u= (9).

A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α=0.01​, is there enough evidence to support the​ researcher's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

Suppose that P(A') = 0.4, P(B') = 0.5, P(An B) = 0.4. Find P(A), P(B), P(AUB), P(An B') and P(AIB).

A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α=0.10 is there enough evidence to support the​ researher's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below. Male 1 2 3 4 5 6 7 8 9 10   Sprint time​ (without nap) 3.92 4.05 4.03 4.06 4.09 3.93 4.02 4.03 3.97 4.09   Sprint time​ (with nap) 3.80 3.99 3.94 3.99 4.06 3.81 3.87 3.90 3.85 3.96     (a) Identify the claim and state H0 and Ha.   What is the​ claim?     A. A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20…

A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α=0.05​, is there enough evidence to support the​ researcher's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α=0.05​, is there enough evidence to support the​ researcher's claim? Assume the samples are random and​dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α=0.10​, is there enough evidence to support the​ researcher's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1

b) Data was collected on 344 corporate executives to find out the effect of MBA degree and work experience on their salary. The following model was estimated: Y = 2.3501 + 3.6306D11 – 2.6354 D2i + 0.8527 X¡ + 1.634 (D, * X)i (2.1805) (- 3.457) (1.263) (7.605) (2.98) R? = 0.8968 Y: Annual Income in Lakhs of Rupees Di and D2 are MBA and gender dummies respectively X: Work experience in years DI = 1 if one has MBA degree = 0 otherwise D2 = 1 for a female executive = 0 for a male executive i. Write the regression equations for female MBA executives and male MBA executives separately. ii. Find the mean income level for the reference category and interpret it. iii. Test the statistical significance of differential intercept coefficient between female MBA executives and Male MBA executives at 5% level of significance. iv. Interpret the coefficient of D,*Xi.