Математика. Материалы курса

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Section "Random variables". Topic "Distribution Laws of Continuous Random Variables".

 Mini-test. 

The first question. A continuous random variable is …

Answers are given. Select the correct one. The second question. The time for carrying out a test task is a random variable… Answer options: discrete, continuous, independent, dependent. Choose the correct answer.

And now to question three. The distribution law of a continuous random variable… Possible answers: binomial, Poisson, geometric, normal. Choose the correct option.

 Let's check your answers. Question One. The correct answer is number three. Question Two. The correct answer is number two. Question Three. The correct answer is number four. The Normal distribution law can be constructed in Excel macros using the category function Statistical NORMS.RASP.

Consider this function in the following example. Plot the graph of the normal distribution function f(x) for x varying from 19.8 to 28.8 in increments of 0.5 if a=24.3 and =1.5.

 Go to the functions of the Statistical category and select the NORM.RASP function. Here you select the first value for X - 19.8, the average value – 24.3. We do it manually. The standard deviation or the average square deviation is 1.5.

 The value of the function is 0.003. Now let's try to do this in Excel. Here is the first resulting value. In order to get the remaining ones, use the mouse pointer to copy the NORM.RASP function by dragging the lower-right corner of the table cursor.

 The range from B3 to B20. We’ve got a column of function values. Let's build a graph. To do this, we select a range of X values and function values. On the Insert ribbon, select Chart and select Point. The resulting graph of the function is the desired one. On the Ox axis there are the values of x, on the ordinate axis there are the values of the constructed function responsible for the normal distribution. I offer tasks for you to solve independently.

Plot the normal distribution density function f(x) for x varying from 20 to 40 in increments of 1 if =3. What I want to draw your attention to. After you build the column by X, don't forget to find the value of the average by X.

 You can use either the corresponding statistical function or Descriptive statistics from the analysis package.

 Task Two. Measurements of the distance to the object are accompanied by systematic and random errors.

 The systematic error is 50 m in the direction of understating the range. The random error follows a normal distribution with an average square deviation of =100 m. Find the probability that the measured distance will not exceed the true one.