# May I know how to solve it?? Thank you

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The moment generating function of X is M(t)=#(e^2t-e^6t)//t(6-2)# .

a) what is the distribution of X?

b) find P(2#<=X<=3)# .

c)the p.d.f for uniform distribution is f(x)= 1/(b-a) for #a<=x<=b# .

Show that the #mu=(a+b)//2 and theta^2=(b-a)^2//12# .

The moment generating function of X is M(t)=

a) what is the distribution of X?

b) find P(2

c)the p.d.f for uniform distribution is f(x)= 1/(b-a) for

Show that the

##### 1 Answer

Recognize that

#### Explanation:

As you stated, for a continuous random variable

The moment generating function is

(a) Therefore,

(b) The probability is

(c) In the general case, the mean is

The mean is also the "first moment"

The second moment is

The variance