無年度 - 主題課程_商學院統計：動差生成函數#107834

科目：主題課程專用 | 選擇題數：0 | 申論題數：25

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所屬科目：主題課程專用

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申論題 (25)

Let X be a random variable with probability density function given by

627ca498e933b.jpg#s-183,58

Find the moment generating function for X.

If the moment generating function of X is M(t) = 0.45 +

627ca56603754.jpg#s-45,22

, what is E(X) and variance of X?

The moment-geterating function of X is

627ca5d823534.jpg#s-144,24

. What are the p.d.f. of X as well as the expectation E(X) and variance Var(X)? (Please show the details)

(a) What is variance of the distribution of X?

(b) What is moment generating function of X?

(1) Find the moment-generating function of Y.

(2) Find the probability density function (pd) of Y.

1

2

The joint pdf of the two continuous random variables X and Y is given by for

0

if it exists. Using the moment-generating function, compute E(X), E(X), and

Cov(X,Y)

(a)

(b)

(c)

(d)

(e)

(a)

(b)

(c)

(d)

(e)

(f)

(a) Find the joint density of the random vector (X,Y).

(b) Find the joint density of the random vector (X,T).

(c) Find the marginal density of T.

(d) Find the conditional density of X given T = 1.