所屬科目：【阿摩】未分類題庫
(a) A student randomly draws one of the coins from the box, what is the probability that it is the fair coin?
(b) Suppose that the student flips the same coin and it shows head. What is the probability that it is the fair coin?
(a) Is \( N \) a discrete random variable or continuous random variable?
(b) What is the probability mass function (PMF) of \( N \)?
(c) What is the cumulative distribution function (CDF) of \( N \)?
(d) What is the PMF of \( N_{B} \)?
(e) What is the expectation of \( N_{B} \)?
(a) Let \( W = \max(X, Y) \). What is the PMF of \( W \)?
(b) What is the CDF of \( W \)?
(c) What is the expectation of \( W \)?
4. (5%) FX(x) is a cumulative distribution function (cdf). Is it true that FX(∞) = 1? (Answer yes or no).
(a) Find the marginal cdf's.
(b) Find the probability of the event \( A = \{X > x, Y > y\} \).
(a) Find the expected value of Y.
(b) Find the variance of Y.
(a) Find c.
(b) Find cdf of X.
(c) Find the variance of X.
(a) Find cdf of X.
(b) Plot pdf of X.
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