SOLUTION: Excel RAND Function. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers betw

Question 1197784: Excel RAND Function. Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.
f(x) 5 51 0
for 0 # x # 1 elsewhere
a. Graph the probability density function. b. What is the probability of generating a random number between .25 and .75? c. What is the probability of generating a random number with a value less than or equal to .30?
d. What is the probability of generating a random number with a value greater than .60?
e. Generate 50 random numbers by entering =RAND() into 50 cells of an Excel worksheet.
f. Compute the mean and standard deviation for the random numbers in part (e).

Answer by onyulee(41) (Show Source): You can put this solution on YOUR website!
**a. Graph the probability density function**
* The probability density function (PDF) for a uniform distribution between 0 and 1 is a rectangle.
* It has a constant height of 1 between x = 0 and x = 1, and 0 elsewhere.
**b. Probability of generating a random number between .25 and .75**
* Since the PDF is a rectangle with a constant height of 1, the probability is simply the width of the interval:
* Probability = 0.75 - 0.25 = 0.50
**c. Probability of generating a random number with a value less than or equal to .30**
* Probability = 0.30 - 0 = 0.30
**d. Probability of generating a random number with a value greater than .60**
* Probability = 1 - 0.60 = 0.40
**e. Generate 50 random numbers in Excel**
1. Open a new Excel worksheet.
2. In cell A1, enter the formula `=RAND()`.
3. Press Enter.
4. Select cell A1 and drag the fill handle (the small square at the bottom right corner of the cell) down to cell A50. This will fill cells A1 to A50 with 50 random numbers.
**f. Compute the mean and standard deviation for the 50 random numbers**
1. In another cell (e.g., B1), enter the formula `=AVERAGE(A1:A50)` to calculate the mean.
2. In another cell (e.g., B2), enter the formula `=STDEV.S(A1:A50)` to calculate the standard deviation.
**Note:**
* The `RAND()` function generates new random numbers every time the worksheet is recalculated.
* To "freeze" the generated numbers, you can copy and paste the values (using "Paste Special" -> "Values") into another set of cells.
**Expected Results:**
* The mean of a large number of uniformly distributed random numbers between 0 and 1 should be approximately 0.5.
* The standard deviation should be approximately 0.2887.
This exercise demonstrates the basic properties of the uniform distribution and how to use Excel to generate and analyze random numbers.

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