# math homework

**ProfArgeol**

** **

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

, if

, if

, if

**2. ****Let be given by its distributionfunction F(x), such that**

**F(x) = 0 if x ≤ 0**

**F(x) = ****if 0<x≤2**

**F(x) =1 if x>2**

** **

**a) ****Graph the distribution function **

**b) ****Graph the density function**

**c) ****Find ,, **

** **

**3. ****A random variable is distributed normally with E(X) = 8 and σ(X) =3****.FindP(9≤X<11). **

** **

**4. ****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.**

** **

** **

**5. ****The density function of a random variable is given by **

** **

** **

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

** **

** **

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

** **

** **

**7. ****It’s known that a random variable is distributed normally with E(X) = 3 and it’s also known that p(0≤X≤1)+p(5≤X≤6) = 0.6. Find p(p(5≤X≤6). **

** **

** **

**8. ****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

**100% ACCURATE ANSWER RELIABLE A++ TUTORIAL PLAGIARISM FREE PERFECT GUIDE**

Purchase the answer to view it

- solution.docx

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

NOT RATED1. 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 …

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

NOT RATEDPreview

5 years ago