# Find if a random variable is given by its density function, such that

**tutor4helpyou**

1. Find , , if a random variable is given by its density function, such that

, if

, if

, if

1. Let be given by its distribution function F(x), such that

F(x) = 0 if x â‰¤ 0

F(x) = if 0<xâ‰¤2

F(x) =1 if x>2

a) Graph the distribution function

b) Graph the density function

c) Find ,,

2. A random variable is distributed normally with E(X) = 8 and Ïƒ(X) =3.FindP(9â‰¤X<11).

3. The distribution of the width of a standard piece of computer paper is normal with an expectation of 8.5 inchesand the standard deviation of 0.2 inch.

a) Find the probability that thewidth of any given piece of computer paper is between 8.40and 8.55.

b) Find the probability that the width of any given piece of computer paper is less than 8.35.

c) Find the probability that the width of any given piece of computer paper is greater than 8.6.

4. The density function of a random variable is given by

Find its (a) math expectation, (b) variance and (c) distribution function.

5. Find the density function of a normally distributed random variable, if E(X) = 7.8 and Ïƒ(X) = 4.1

6. Itâ€™s known that a random variable is distributed normally with E(X) = 3 and itâ€™s also known thatp(0â‰¤Xâ‰¤1)+p(5â‰¤Xâ‰¤6) = 0.6. Find p(5â‰¤Xâ‰¤6).

7. Describe a real-life situation to which the normal distribution could be applied. Explain why. How does a normal distribution differ from one, which is not? Which aspects of your situation might be altered?

- 7 years ago

**Find if a random variable is given by its density function, such that**

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### Find E(x),Var(x) if a random variable is given by its density function , such that

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6 years ago