A Random Variable In Tasks 9-18 you are asked to conduct some computations regar

Question

A Random Variable
In Tasks 9-18 you are asked to conduct some computations regarding a random variable. Use the (incomplete) table below as the definition of this random variable (after you fill in the blank). The sample space of a random variable is comprised of the integers 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value are shown in the table below (with one missing value).

Value

0

1

2

3

4

5

6

Probability

.10

.15

.25

.10

.10

.15

A Random Variable:

9.   The missing probability value (under the number 4) in the random variable table above is:_______

10.   The sum of the probabilites in the second row of any random variable table like the one above should equal (round to 3 decimal places): _______________________________________________.

11.   Read section 4.4.1 in the book (Yakir, 2011). Do the numbers in the table above (for the random variable) represent a data sample (Yes/No)?____

12.   In the random variable table shown above, the value in the second row represents the cumulative probability of the corresponding values in the first row (True/False) _________

13.   The probability that a randomly selected value from this random value will be less than or equal to 3 is :_____.

14.   What is the probability that a randomly selected value from the random variable would be exactly 1.5? ___________ .

15.   Review section 4.4 in the book (Yakir, 2011), especially pages 57—58. The expectation of the random variable is:______.

16.   To find the expectation of a random variable by using a relative frequency table, you can add the values in the first row of the table and divide by the number of columns in the table (True/False)_________.

17.   Study Yakir (2011) pp. 57-59 and solved problems 4.1.6-4.1.8. The (population) standard deviation of the random variable above is (round to 3 decimal places):_______ (hint, you cannot put values from the table into the sd() function because the sd() function does not adjust for the probabilities).

18.   If you have already calculated the standard deviation of a data sample, what is the next thing to do to find the variance: ______________________________.

Value

0

1

2

3

4

5

6

Probability

.10

.15

.25

.10

.10

.15

Explanation / Answer

9. The missing probability value (under the number 4) in the random variable table above is:
= 1 - (.10+.15+.25+.10+.10+.15) = 0.85

10. The sum of the probabilites in the second row of any random variable table like the one above should equal (round to 3 decimal places):
= .15+.25+.10+.10+.15+0.15 = 0.9

12. In the random variable table shown above, the value in the second row represents the cumulative probability of the corresponding values in the first row (True/False) _________
it is false

13. The probability that a randomly selected value from this random value will be less than or equal to 3 is :_____.
=.10+.15+.25+.10 =0.60

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