3.(a) (8%) Find the eignevalues and eigenvectors for

(b) (3%) How can you tell whether a matrix is invertible from its eigenvalues?

(c) (3%) How can you tell whether two matrices are similar from their eigenvalues?

4. (a) (8%) For the following matrix, find the bases for its row space and nullspace.

(b) (3%) In R3, is xy plane orthogonal to xz plane ? Explain it.

5. (12%) Let random variable X be uniformly distributed in [-2,2]. Find , the probability density function of Y = X2 for y＞0.

6. (13%) Let X and Y be independent exponentially distributed random variables with common parameter λ. Find the probability density function of Z = X+Y.

(a) (10%) Find the marginal PMF of X in terms of N and C.

(b) (5%) If N=3, find C.

(c) (10%) If N=3 and Z= X(N-X), find , the PMF of Z, for all z.

1. A recent report claims that college non-graduates get married at an earlier age than college graduates. To support the claim, tandom samples of size 100 were selected from each group, and the mean age at the time of marriage was recorde(D) The mean and standard deviation of the college non-graduates were 21.6 years and 3 years, respectively, while the mean and standard deviation of the college graduates were 23.2 years and 4 years, respectively. To test the claims of the report at the 0.05 level of significance, the figure of the appropriate test statistic is__________.

101年 - 101 國立交通大學_碩士班考試入學試題_電機工程學系：線性代數與機率#105746