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__________.

2. Let the joint probability function of X and Y be given by P(X=1|Y=2)=_________.

3. Customers enter a restaurant at random at a rate of four per minute. Assume that the number entering this restaurant in any given time interval has a Poisson distribution. The probability that at least two customers enter the restaurant in a given 0.25-minute interval is__________.

4. A random variable X represents the number of defective mobile phone is a shipment of four iPhones to a local mobile phone store. Assume that each mobile phone is equally likely to be defective or non-defective, and also assume that each mobile phone is defective or non-defective independently of the other mobile phones. Then the expected number of defective mobile phones 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