98年 - 98 國立交通大學管碩士班考試入學試題_交通運輸研究所、運輸科技與管理學系：統計學#124074

(a) Find the mean value and variance of Y₁ = X₁ + X₂.
Answer: Mean = __( A )__ ； Variance =__( B )__

(b) Find the mean value and variance of of Y₂ = 2X₁.
Answer: Mean = __(C)__ ； Variance =__(D)__

(a) The (marginal) probability mass function of X, pₓ(x) =__(E)__.

(b) The (marginal) probability mass function of Y, pᵧ(y) =__(F)__.

(c) Are X and Y independent? Answer=__(G)__.

(a) The expected value of X, E(X) = __(H)__.

(b) The expected value of Y, E(Y) =__(I)__.

(c) The covariance, Cov(X,Y) =__(J)__.

(a) If two or more of the six devices in the Administration building are activated during the same weekend, the system automatically signals the police. What is the probability that this system will signal the police next weekend?
Answer=__(K)__. Hint: remember the assumption.

(b) An intruder has a 5% chance of not activating the device located in the President's office.
Campus police has obtained information about a student prank in preparation and, as a result, estimates that there is a 20% chance that an intruder will visit the President's office during next Columbus Day weekend. If this device is activated during that weekend, what is the probability that there is an intruder in the President's office? Answer=__(L)__

(a) What is the probability that a new policy holder has an accident the first year?
Answer=__(M)__.

(b) What is the probability that a new policy holder that does not have an accident in the first year is unsafe?
Answer=__(N)__.

(a) Use the properties of a pdf to find the value of k.
Answer=__(O)__.

(b) Find an expression for P(X≥ t).
Answer= __(P)__.

(c) Find an expression for P(X≥t + s| X≥s).
Answer=__(Q)__.

7. In Saracho's study, the mean score achieved by a sample of 16 sixth-grade girls who had received computer-assisted instruction was 7.08 with a standard deviation s of 1.93. Assuming that the sample is representative of the population and assuming that the population is normally distributed, compute the 95% confidence interval for the mean μ of the population. (The critical value of t is 2.131.)
Answer=__(R)__.

(a) Write a complete equation for the simple linear regression model that incorporates the estimated coefficients provided by this computer output. Make sure to define in words all the variables used in this equation.
Answer=__(S)__.

(b) Interpret, in managerial terms, the meaning of each of the two regression coefficients
(including the units in which each is expressed).
Answer=__(T)__.

(a) The Null Hypothesis, and the Alternative Hypothesis. 5%
You compute SST (Total Sum of Squares), SSG (Group Sum of Squares) and SSE (Error Sum of Squares), and determine DF (Degrees of Freedom) to test the hypothesis. The Level of Significance:
α = 0.05.

(b) Complete the following ANOVA table. 5%

(a) Moment Generating Function, M(t) = 4%

(b) Mean, E(X) = 3%

(c) Variance, Var(X) = 3%