Question

All are multiple choice quesions

1.   Probability is
A. Subjective judgement of the observer, how likely is something.;
B. A measure rendered (adjusted to events) satisfying certain rules;
C. Empirical, observed result of the (favorable) over (all) cases;
D. Any number between 0 and 1;

   2. Which statement is true regarding sample standard deviation?
   Sample standard deviation is the expected value of the smallest and the largest observations
   Standard deviation of the sum of two random variables equals with the sum of the standard deviation
   Standard deviation of the expected value is always zero
   Standard deviation of the mean is always zero

   3. With the help of standardization,
   Any given distribution can be transformed into normal distribution
   Any given distribution can be transformed into standard normal distribution
   Any normal distribution with given parameters can be transformed into standard normal distribution
   A standard normal distribution can be transformed into a distribution with 1 expected value and 0 standard deviation

   4. Distribution function of a ξ random variable
   The function value is 0 in -∞ and 1 in +∞
   F(x)=P(ξ=x) defines the distribution function of ξ
   According to the definition, the function value for every x is represent the probability that ξ is larger than the value x
   Area under the distribution function is always 1

   5. The expected value of a random variable
   The expected value of a random variable depends on distribution and the range of a given random variable.
   The expected value of a random variable is always and existent representation of the random variable
   The value of two random must be the same when the expected value of the variables equals
   In case of limited number of observations, The expected value of a random variable equals with the mean

6. In the least square method

1. The sample stardard deviation of the squares of distances of data points on the y-axis is minimal
2. The sum of squares of the distances of the data points on the y-axis is minimal
3. The squares of the distances of the worst fitting points on the y-axis are minimal
4. The median of the squares of the distances of the data points on the y-axis is minimal

7. Binary data

1. May take only 2 different values;
2. Contains only digital numbers;
3. Based on number system two;
4. May assume any number;

8. Population is

1. All the humans of a territory;
2. All the objects examined in detail by the statistician;
3. Well defined group of objects, where potentially all of them could be studied in details;
4. Any group of objects, any mathematical set;

Answer 1

1)

Any number between 0 and 1

Observed favorable over all cases ... Both statement are true , but any number between 0 and 1is more accurate here

2)

Standard deviation of the sum of two random variables equals with the sum of the standard deviation

3)

Any given distribution can be transformed into standard normal distribution

4)

The function value is 0 in -∞ and 1 in +∞

5)

The expected value of a random variable depends on distribution and the range of a given random variable.

6)

The sum of squares of the distances of the data points on the y-axis is minimal

7)

May take only 2 different values

8)

defined group of objects, where potentially all of them could be studied in details

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