Variant 18
1. A coin is tossed four times. Find the probability that a) the coin lands on heads three times; b) the coin lands on tails twice.
2. There are radio tubes made by two factories on a warehouse. 60 % of them are made by the first factory and 40 % – by the second. It is known that 85 of 100 tubes made by the first factory satisfy the standard, and 75 of 100 tubes made by the second factory satisfy the standard. Determine the probability that a randomly taken tube from the warehouse will satisfy the standard.
3. Assuming that the probability of landing six aces at one tossing a die is equal to 1/6, determine the probability that in a series of 100 tossings the die lands on six aces: a) exactly 20 times; b) from 18 up to 30 times.
4. The laws of distribution of two independent random variables are given by the following tables of distribution:
X |
–2 |
–1 |
0 |
|
Y |
–1 |
0 |
1 |
P |
0,1 |
0,6 |
0,3 |
|
P |
0,4 |
0,1 |
0,5 |
Compose the law of distribution of their product and check the following property: M(X Y) = M(X) M(Y).
5. A random variable X is given by the integral function:
Find: a) the differential function f(x); b) the mathematical expectation and the dispersion of X; c) the probability of hit of the random variable into the interval (2; 5).
6. The mathematical expectation and the dispersion of a normally distributed random variable X are equal to 26 and 9 respectively. Find: a) the probability that the random variable X will take on a value from the interval (20; 29); b) the probability that the deviation X – M(X) will be no more than 1 by absolute value.
7. The discrete random variable X is given by the law of distribution:
-
X
2
3
4
P
0,6
0,1
0,3
By using the Chebyshev’s inequality estimate the probability that the absolute value of deviation of the random variable from its mathematical expectation less than 3.
8. The following data on monthly loading (in hours) of a separate worker have been received after inspecting 100 commercial banks:
771 |
753 |
762 |
751 |
761 |
735 |
772 |
743 |
746 |
756 |
751 |
761 |
752 |
786 |
752 |
775 |
756 |
797 |
771 |
772 |
775 |
764 |
749 |
767 |
763 |
758 |
762 |
762 |
747 |
763 |
764 |
774 |
766 |
772 |
777 |
767 |
773 |
761 |
746 |
757 |
759 |
761 |
787 |
752 |
799 |
761 |
798 |
752 |
761 |
787 |
756 |
739 |
778 |
793 |
768 |
771 |
778 |
788 |
781 |
771 |
759 |
787 |
775 |
747 |
753 |
748 |
754 |
761 |
762 |
764 |
785 |
764 |
763 |
765 |
753 |
755 |
758 |
786 |
761 |
775 |
766 |
761 |
752 |
745 |
771 |
754 |
799 |
769 |
738 |
749 |
743 |
755 |
777 |
758 |
774 |
778 |
763 |
789 |
747 |
754 |
1) Compose the interval and the discrete variation series taking the beginning of the first interval equal 730, and the width of each interval equal 10.
2) Construct the histogram and the polygon of relative frequencies of distribution.
3) Find the mode and the median (using the discrete series).
4) Find empirical functions of distribution of continuous and discrete variation series; and construct their graphs.